Find the length of x indicated in the figure. give your answer to 3 significant figures.

x = 69.506 cm

Step-by-step explanation:

Let the total length of the base of the big right angle triangle be y cm. Therefore,

The length of the base of the smaller right angle triangle would be y - 67

We would apply trigonometric ratio.

Considering the small, right angle triangle, it becomes

Tan # = opposite side/adjacent side

Tan 55 = x/(y - 67)

1.4281 = x/(y - 67)

x = 1.4281(y - 67)

x = 1.4281y - 95.6827 - - - - - - - - - 1

Considering the big right angle triangle, it becomes

Tan # = opposite side/adjacent side

Tan 31 = x/y

x = ytan31 = y × 0.6009

x = 0.6009y

Substituting x = 0.6009y into

equation 1, it becomes

0.6009y = 1.4281y - 95.6827

95.6827 = 1.4281y - 0.6009y

0.8272y = 95.6827

y = 95.6827/0.8272 = 115.67

x = 0.6009y = 0.6009 × 115.67

x = 69.506

4

step-by-step explanation: