Right Triangles and Trigonometry: Ratios of Right Triangles

Think & Click: Evaluate Trigonometric Expressions With Your Calculator

Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

1. What is tan 45°?

tan 45° = 1

2. What is sin 35°?

sin 35° ≈ 0.57

3. What is sec 32°?

the secant of 32 degrees equals the quotient 1 divided by the cosine of 32 degrees approximately equals the quotient 1 divided by zero point 8 5 approximately equals 1 point 1 8

4. What is cos 67°?

cos 67° ≈ 0.39

5. What is csc 63°?

the secant of 63 degrees equals the quotient 1 divided by the cosine of 63 degrees approximately equals the quotient 1 divided by zero point 8 9 approximately equals 1 point 1 2

6. Solve:

Take the inverse sine of both sides.

the inverse sine of the sine of x equals the inverse sine of zero point 9 7 5

The sine and the inverse sine cancel out.

x equals the inverse sine of equals zero point 9 7 5 approximately equals 77 point 1 6 1 degrees

7. Find the measure of angle B.

Right Triangle

The side adjacent to angle B is 63.
The hypotenuse is 75.
The function that uses the adjacent side and the hypotenuse is cosine, so we can write the equation:

the cosine of B equals the quotient sixty-three-seventy-fifths

Solve this for B.

inverse cosine of the cosign of B equals the inverse of cosine of the quotient sixty-three-seventy-fifths; B equals the inverse of the quotient sixty-three-seventy-fifths approximately equals 32 point 8 6 0 degrees