MFM 2PIUnit 6: Trigonometry

Day 3: Solving Problems Using Trigonometry

Example 1:  Dana's kite string is 35 m long.  It makes an angle of 50o with the ground.  Let x be the horizontal distance, in metres to the kite.  What is the horizontal distance between the kite and Dana?

50°

35 m

x

Have:

Need:

Use:

50°Hyp - 35Adj - x

CAH - cos ratio

∴ The distance is 22.5 m

Example 2: A storm caused a 13.5m hydro pole to lean over. The top of the pole is now 11.8m above the ground. Find the measure of the angle between the hydro pole and the ground, to the nearest degree.

x

13.5 m11.8m

Have:

Need:

Use:

Opp - 11.8Hyp - 13.5angle

SOH - sin ratio

∴ The angle between the pole and the ground is 61°.

To talk about angles we need to have a reference point. Sometimes we use an _____________________________________.

The angle of elevation is the angle of view _________________________________________________.

angle of elevation

from the horizontal up to a point of reference.

Example. 4: You are standing 11.2 m from the wall of the school. The angle of elevation from where you are standing to the top of the school is 37o. Find the height of the school.

37°

11.2 m

x

Have:

Need:

Use:

37°Adj - 11.2Opp - x

TOA - tan ratio

∴ The height of the wall is 8.4 m

Example 5: A truck travels 6 km up a mountain road. The change in height is 0.375 km. What is the measure of the angle of elevation?

Have:

Need:

Use:

Opp - 0.375Hyp - 6angle

SOH - sin ratio∴ The angle of elevation of the road is 3.6°.

The _______________________________ is the angle of view ____________________________________

angle of depressionfrom the horizontal down to a reference point.

Example 6: The highest point along the cliff of the Cathedral Bluffs in Toronto is 90 m above the shore. From the top of the cliff a surveyor spots a boat out in the lake, at an angle of depression of 43o. How far is the boat from the shore, to one decimal place?

43°

43°

This angle is also 43° because of the z-rule of parallel lines

x

90 m

Have:

Need:

Use:

43°Opp - 90Adj - x

TOA - tan ratio

∴ The boat is 96.5 m from shore.

Example 7: Suppose a plane is coming down for a landing at the Region of Waterloo International Airport. The angle of depression is 22o . The plane is 350 m from the landing point along the ground. How high is the plane?

22°

22°

350 m

h

Have:

Need:

Use:

22°Adj - 350Opp - x

TOA - tan ratio

∴ The plane is 141.4 m above the ground.

Example 8: Two students want to determine the heights of two buildings. They stand on the roof of the shorter building. The students use a clinometer to measure the angle of elevation to the top of the taller building as 50o. From the same position, the students measure the angle of depression to the base of the taller building as 30o. They measure the horizontal distance between the two buildings to be 43.3 m. How tall is each building?

50°30°

43.3 m

43.3 m

x

yTop Triangle Bottom Triangle

Have:

Need:Use:

50°Adj - 43.3Opp - yTOA - tan ratio

Have:

Need:Use:

30°Adj - 43.3Opp - xTOA - tan ratio

∴ The taller building is 76.6 m high and the shorter building is 25 m high

Homework: pg. 86 – 87 #2 – 11