(a) State the exact values for the six trigonometric ratios of angle (theta) in the triangle below. (b) Find the value of angle , to the nearest degree.

Question

In the diagram given there is a right-angle triangle, on the side with the right angle it says 2 square root 10 cm. on the side that looks the longest, it says square root 48 cm. and inside there is  (theta).

Answer 1

θ could be one of two complementary angles, so I’ll start with one angle and then complement it in case you meant the other angle.

First, let’s calculate the length of the remaining side:

√(48-(2√10)²)=√(48-40)=√8=2√2.

(a)

sinθ=2√10/√48=2√(10/48)=2√/(5/24)=√⅚; cosecθ=√⁶⁄₅ or √1.2.

cosθ=2√2/√48=2√(1/24)=√⅙; secθ=√6.

tanθ=sinθ/cosθ=√5; cotθ=√5/5 (same as 1/√5).

(b)

θ=arctan(√5)=65.9, or 66° to the nearest degree.

The “other” θ is 24° to the nearest degree and the trig ratios are:

(a)

sinθ=√⅙; cosecθ=√6.

cosθ=√⅚; secθ=√⁶⁄₅ or √1.2.

tanθ=√5/5 (same as 1/√5); cotθ=√5.