Question

Can someone please help me find the missing side?

Answer 1

6.20 units to the nearest hundredth.

Explanation:

WE apply the trigonometry of a right angled triangle.

Consider the larger triangle where we can find the length of the side opposite to the 53 degree angle:

sin 53 = y / 30 (where y = length of the opposite side mentioned.)

y = 30 sin 53 = 23.96 units.

Now consider the smaller triangle where side y is the hypotenuse:

cos 75 = x / y

cos 75 = x / 23.96

x = 23.96 cos 75

= 6.20 units.

Answer 2

x ≈ 6.2

Explanation:

To find x using trig. ratios we require to find the hypotenuse of the right triangle on the left.

From the right triangle on the right we can calculate the hypotenuse.

sin53° =
`(opposite)/(hypotenuse)` =
`(opp)/(30)`

Multiply both sides by 30

opp = 30 × sin53° ≈ 24

Thus the length of the hypotenuse of the triangle on the left is 24, hence

cos75° =
`(adjacent)/(hypotenuse)` =
`(x)/(24)`

Multiply both sides by 24

x = 24 × cos75° ≈ 6.2