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A farmer has a triangular field where two sides measure 450 yards and 320 yards. The angle between these two sides measures 80º. The farmer wishes to use an insecticide that costs $4.50 for every 100 square yards. What will it cost to use this insecticide on this field?
Law of SinesLaw of Sines
Students will be able to…use the Law of Sines to solve triangles and real-world problems.
In the past you’ve used trig to solve right triangles.
To solve a triangle with no right angle, you need to know the measure of at least one side and any two other
parts of the triangle.
Works in the following cases:› ASA (Angle-Side-Angle)› AAS (Angle-Angle-Side)› SSA (Side-Side-Angle) **this could be the
ambiguous case
In trigonometry, we can use theLaw of Sines to find missing parts of triangles that are not right triangles.
Law of Sines:In ABC,
sin A = sin B = sin C a b c
B
A
C
cb
a
Find p. Round to the nearest tenth.
Law of Sines
Use a calculator.
Divide each side by sin
Cross products
Answer:
Law of Sines
Cross products
Divide each side by 7.
to the nearest degree in ,
Solve for L.
Use a calculator.
Answer:
a. Find c.
b. Find mR to the nearest degree in RST if r = 12, t = 7, and mT = 76.
Answer:
Answer:
The Law of Sines can be used to “solve a triangle,” which means to find the measures of all of the angles and all of the sides of a triangle.
We know the measures of two angles of the triangle. Use the Angle Sum Theorem to find
. Round angle measures to the nearest degree and side measures to the nearest tenth.
Angle Sum Theorem
Subtract 120 from each side.
Add.
Since we know and f, use proportions involving
To find d:
Law of Sines
Cross products
Substitute.
Use a calculator.
Divide each side by sin 8°.
To find e:
Law of Sines
Cross products
Substitute.
Use a calculator.
Divide each side by sin 8°.
Answer:
We know the measure of two sides and an angle opposite one of the sides.
Law of Sines
Cross products
Round angle measures to the nearest degree and side measures to the nearest tenth.
Solve for L.
Angle Sum Theorem
Use a calculator.
Add.
Substitute.
Divide each side by 16.
Subtract 116 from each side.
Cross products
Use a calculator.
Law of Sines
Divide each side by sin
Answer:
Answer:
a. Solve Round angle measures to the nearest degree and side
measures to the nearest tenth.
b. Round angle measures to the nearest degree and side measures to the nearest tenth.
Answer:
A 46-foot telephone pole tilted at an angle of from the vertical casts a shadow on the ground. Find the length of the shadow to the nearest foot when the angle of elevation to the sun is
Draw a diagram Draw Then find the
Since you know the measures of two angles of the
triangle, and the length of a side
opposite one of the angles you
can use the Law of Sines to find the length of the shadow.
Cross products
Use a calculator.
Law of Sines
Answer: The length of the shadow is about 75.9 feet.
Divide each side by sin
A 5-foot fishing pole is anchored to the edge of a dock. If the distance from the foot of the pole to the point where the fishing line meets the water is 45 feet, about how much fishing line that is cast out is above the surface of the water?
Answer: About 42 feet of the fishing line that is cast out is above the surface of the water.
