Applying SOHCAHTOA

Applying Trigonometric Models to Solve Problems

C. McCarthy

Dev.Cur.Mat.Mod5

January, 2004

Objective

• To practice applying right triangle models to word problem or real life situations.

• To practice using the right angle definitions of the trigonometric functions to solve for the needed information.

S O H C A H T O A

• We have already looked at the acronym for remembering the right angle definitions of the trigonometric functions. Until you have internalized these definitions, it is helpful to write the acronym on your paper and punctuate appropriately to use as you are solving these problems.

S=O/H C=A/H T=O/A

• Consider the following application exercise from the textbook (4.8, #30):– From a point on level ground thirty yards from

the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.

– First, identify the question and the given information.

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.

– First, identify the question and the given information.

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.

– First, identify the question and the given information.

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.– Then consider a right triangle model that will

allow us to solve the problem. In this case the triangle would be described by the given point, the base of the building, and the top of the building.

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.– Make a sketch of your model

– Change units if necessary

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.– Make a sketch of your model

– Change units if necessary

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.– We are asked to find the height, or the length of the

side opposite the given angle.

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.– We are asked to find the height, or the length of the

side opposite the given angle.

– We are given the angle

– and the adjacent side.

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.– We are asked to find the height, or the length of the

side opposite the given angle.

– We are given the angle

– and the adjacent side.

– Use T=O/A

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.– Use T=O/A

– Tan(38.7º)=h/90

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.– Use T=O/A

– Tan(38.7º)=h/90

– Isolate h

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.– Use T=O/A

– Tan(38.7º)=h/90

– Isolate h - h=90tan(38.7º)

S=O/H C=A/H T=O/A

• From a point on level ground thirty yards from the base of a building, the angle of elevation is 38.7º. Approximate the height of the building to the nearest foot.– Use T=O/A

– Tan(38.7º)=h/90

– Isolate h - h=90tan(38.7º)

– Use TI-83+ to solve

– (or another method)

S=O/H C=A/H T=O/A

• Consider another application exercise from the textbook (4.8, #35):– A wheelchair ramp is to built beside the steps to

the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.

S=O/H C=A/H T=O/A

A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– First, identify the question and the given

information.

S=O/H C=A/H T=O/A

A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– First, identify the question and the given

information.

S=O/H C=A/H T=O/A

A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– First, identify the question and the given

information.

S=O/H C=A/H T=O/A

A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.

Then consider a right triangle model that will allow us to solve the problem. In this case the triangle would be described by the ramp, the ground underneath, and the six foot segment.

S=O/H C=A/H T=O/A

A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.Make a sketch of your model.

S=O/H C=A/H T=O/A

• A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– Make a sketch of your model

S=O/H C=A/H T=O/A

• A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– Make a sketch of your model

– We want to find the angle of elevation.

S=O/H C=A/H T=O/A

• A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– Make a sketch of your model

– We want to find the angle of elevation.

– We are given lengths of the hypotenuse and the opposite side.

S=O/H C=A/H T=O/A

• A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– Make a sketch of your model

– We want to find the angle of elevation.

– We are given lengths of the hypotenuse and the opposite side.

– Use S=O/H

S=O/H C=A/H T=O/A

• A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– Use S=O/H

– Sin(x) = 6/23

S=O/H C=A/H T=O/A

• A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– Use S=O/H

– Sin(x) = 6/23

– Sin-1(0.26087) = x

S=O/H C=A/H T=O/A

• A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– Use S=O/H

– Sin(x) = 6/23

– Sin-1(0.26087) = x

– X = 15.12º

S=O/H C=A/H T=O/A

• A wheelchair ramp is to built beside the steps to the campus library. Find the angle of elevation of the 23 foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.– Use S=O/H– Sin(x) = 6/23– Sin-1(0.26087) = x– X = 15.12º– Round to 15.1º

Assignment:

• Write 5 different word problems that can be solved using the right angle definitions of trigonometric functions.

• For full credit, problems should– Describe different situations.

– Request information more difficult to measure than the given information.

– Be interesting or practical - preferably both.

• The best questions will be used on the final exam.