Question

8. The figure shows an isosceles triangle TUV where
TU = TV = 9.6 m and UV = 15.4 m. Find the height,
TH, of the triangle.
T
9.6 m
H
U
15.4 m -​

Answer 1

Given:

The figure shows an isosceles triangle TUV where  TU = TV = 9.6 m and UV = 15.4 m.

To find:

Find the height,  TH, of the triangle.

Solution:

From the given information, we have the data as follows.

The figure shows an isosceles triangle TUV where  TU = TV = 9.6 m and UV = 15.4 m.

Consider the attached figure while going through the following steps.

From the figure it's clear that,

UH = HV = UV/2

UH = HV = 15.4/2

UH = HV = 7.7 m

Consider the Pythagoras theorem.

TU² = TH² + UH²

TV² = TH² + VH²

9.6² = TH² + 7.7²

92.16 = TH² + 59.29

TH² =  92.16 - 59.29

TH² = 32.87

TH = 5.73 m

Therefore, the value of TH is 5.73 m.