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Math 1330 Section 7. Solving Right Triangles
In this section, we’ll solve right triangles. We’ll use right triangle trigonometry to find the lengths of all of the sides and the measures of all of the angles. In some problems, you will be asked to find one or two specific pieces of information, but often you’ll be asked to “solve the triangle,” that is, to find all lengths and measures that were not given.
You’ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of 30 ° − 60 °− 90 °triangles or of 45 ° − 45 °− 90 °triangles.
Example 1: Write and solve two trigonometric functions to find x and y.
y
x
60 °°°° 12
Example 2: Use properties of special triangles to find x and y.
y
5 3
x
60 °°°°
Example 3: Suppose x represents an acute angle in a right triangle. Use a calculator to find x and round to the nearest hundredth.
sin( x )=. 5824
Example 4: Suppose x represents an acute angle in a right triangle. Use a calculator to find x and round to the nearest hundredth.
tan( x )=
Example 5: Find x and round the answer to the nearest hundredth.
19
x
(^56) °°°°
Example 6: In ∆ ABC with right angle C , ∠ A = 31 °and AC = 18. Find BC. Round the answer to the nearest hundredth.
Example 7: Solve the triangle. Round all answers to the nearest hundredth.
12 D
A
B
29 °°°°
Example 11: Draw a diagram to represent the given situation. Then find the indicated measure to the nearest tenth.
The angle of elevation to the top of a building from a point on the ground 75 feet away from the building is 12°. How tall is the building?
Example 12: Draw a diagram to represent the given situation. Then find the indicated measure to the nearest tenth.
Dave is at the top of a hill. He looks down and spots his car at a 53° angle of depression. If the hill is 82 meters high, how far is his car from the base of the hill?
