Question

Tower A and B are 151 m apart.

From the top of tower A at 68 m above ground, the angle of elevation to the top of tower B is 23°.
How tall is tower B to the nearest metre?

Answer 1

The height of tower B is approximately 68.47 meters, rounded to the nearest meter.

`\[ \text{Height of Tower B} \approx 68 \, \text{m} \]`

To find the height of tower B, we can use trigonometry. The tangent of the angle of elevation is the ratio of the opposite side (height of tower A) to the adjacent side (distance between towers A and B).

`\[ \tan(23^\circ) = \frac{\text{Height of Tower A}}{\text{Distance between Towers A and B}} \]`

Let
`\( h_B \)` be the height of tower B, then:

`\[ \tan(23^\circ) = (68)/(151) \]`

Solving for
`\( h_B \)`:

`\[ h_B = \tan(23^\circ) * \text{Distance between Towers A and B} + \text{Height of Tower A} \]`

`\[ h_B \approx \tan(23^\circ) * 151 + 68 \]`

`\[ h_B \approx 68.47 \, \text{m} \]`

Answer 2

132m

Explanation:

Height of tower B = Height of tower A + difference in height between tower B and A

The difference in height can be determined using tan

tan 23 = opposite / adjacent

tan 23 = opposite / 151

0.4245 x 151 = opposite

opposite = 64m

Height of tower B = 64m + 68m = 132m