Question

Find the missing side QG. Round answer to nearest tenth.

Answer 1

Answer:

QG = 55.759 ft

QG = 60ft (To the nearest 10th)

Step-by-step explanation:

From the figure, the angles of two sides of the triangle are given.

This makes it pretty easier to solve..

Let's go!

To solve for the length QG, we must first resolve it's corresponding angle using the sine formula.

Okay now!

The sum of angles of a triangle add up to 180°.

Therefore:

Angles QGT° + GQT° + GTQ° = 180°

41° + 67° + GTQ° = 180°

108 ° + GTQ° = 180°

GTQ° = 180° - 108°

GTQ° = 72°

Since we've been able to get that missing angle, we can proceed to solve for the length of QG using the sine formula.

Sin 67° / 54ft = sin 72° / QG

Lets Cross Multiply

QG sin 67° = 54ft sin 72 °

QG * 0.921 = 54ft * 0.951

QG * 0.921 = 51.354

QG = 51.354 / 0.921

QG = 55.759 ft

QG = 60ft (To the nearest 10th)