Question

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

Answer 1

Using the trigonometric ratio:

`\cos \Theta=(adjacent)/(hypotenuse)`

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

substitute the values and evaluate

`\cos 45=(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=(opposite)/(adjacent)`
`\tan 60=(b)/(5)`

cross-multiply

b= 5 tan 60

b=8.66

b≈ 8.7 to the nearest tenth