Question

for the right triangles below, find the values of the side lengths a and b.

Answer 1

Using the trigonometric ratio:

$\cos \Theta=\frac{adjacent}{hypotenuse}$

fromthe question, theta = 45 adjacent = a and hypotenuse = 4

substitute the values and evaluate

$\cos 45=\frac{a}{4}$

cross-multiply

a = 4 cos 45

a = 2.83

a ≈ 2.8 to the nearest tenth

To find b

adjacent = 5 opposite = b and theta =60

Using the trig. ratio

$\tan \Theta=\frac{opposite}{adjacent}$$\tan 60=\frac{b}{5}$

cross-multiply

b= 5 tan 60

b=8.66

b≈ 8.7 to the nearest tenth