Answer: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
