Express sin P, cos P, and tan P using a, b, and c.
Hint
Soak a toe. Ahhh.
Answer
Example 2
What are the three angles of a right triangle with side lengths of 15, 36, and 39?
Hint
One of the angles is 90°, the longest side is always the hypotenuse, and inverse trig functions work wonders.
Answer
22.6°, 67.4°, and 90°
Example 3
What is the length of a right triangle's hypotenuse if the side adjacent to a 78° angle is 1?
Hint
We know an angle's measurement and the length its adjacent side. Which trig function would be best to use?
Answer
Hypotenuse ≈ 4.8
Example 4
Find the value of x and y.
Hint
Use the trig functions on the 58° angle. Different trig functions will solve for different variables.
Answer
x ≈ 8.5; y ≈ 5.3
Example 5
Find the value of x.
Hint
Find the value of both legs of both triangles.
Answer
x ≈ 21.5
Example 6
Find the value of x and y.
Hint
Two different trig functions performed on the same angle should give us both answers.
Answer
x ≈ 20.3; y ≈ 5.6
Example 7
Find all the angles of a triangle with points X (-4, 6), Y (-4, -2), and Z (3, -2).
Hint
The distance formula and grids are always useful. Calculating the length of the hypotenuse is optional.
Answer
41.2°, 48.8°, and 90°
Example 8
Alex is a tightrope walker. He wants to tie a 40-foot rope to two poles so that he can practice for his upcoming circus show. After all, practice makes perfect. The poles are arranged in this way.
To which two poles should he tie his rope if he wants to walk across greatest distance possible?
Hint
Calculating the distance between each pair of poles gives him the options, but his rope is only 40 feet long.
