As part of her assignment, Devi has to use her clinometer to measure the height of an
office tower . From a point , she observes that angle . She then walks 25 m
away from the office tower to a point and observes that angle .
Find the height of the sfice tover.

Ask by Tran Li. in Singapore

Dec 12,2024

Question

As part of her assignment, Devi has to use her clinometer to measure the height of an
office tower . From a point , she observes that angle . She then walks 25 m
away from the office tower to a point and observes that angle .
Find the height of the sfice tover.

Ask by Tran Li. in Singapore

Dec 12,2024

UpStudy AI · Accepted Answer

To find the height of the office tower $$ TA $$, we can use trigonometry based on the angles observed from points $$ B $$ and $$ C $$.

Let:
- $$ h $$ be the height of the office tower $$ TA $$.
- $$ d $$ be the horizontal distance from point $$ B $$ to the base of the tower $$ A $$.

From point $$ B $$, we have:
$$
\tan(34^\circ) = \frac{h}{d}
$$
This can be rearranged to give:
$$
h = d \cdot \tan(34^\circ) \quad \text{(1)}
$$

From point $$ C $$, which is 25 m away from point $$ B $$, the distance from point $$ C $$ to the base of the tower $$ A $$ is $$ d + 25 $$ m. The angle observed from point $$ C $$ is $$ 26^\circ $$:
$$
\tan(26^\circ) = \frac{h}{d + 25}
$$
This can be rearranged to give:
$$
h = (d + 25) \cdot \tan(26^\circ) \quad \text{(2)}
$$

Now we have two equations for $$ h $$:
1. $$ h = d \cdot \tan(34^\circ) $$
2. $$ h = (d + 25) \cdot \tan(26^\circ) $$

Setting the two expressions for $$ h $$ equal to each other:
$$
d \cdot \tan(34^\circ) = (d + 25) \cdot \tan(26^\circ)
$$

Expanding the right side:
$$
d \cdot \tan(34^\circ) = d \cdot \tan(26^\circ) + 25 \cdot \tan(26^\circ)
$$

Rearranging gives:
$$
d \cdot \tan(34^\circ) - d \cdot \tan(26^\circ) = 25 \cdot \tan(26^\circ)
$$
$$
d \cdot (\tan(34^\circ) - \tan(26^\circ)) = 25 \cdot \tan(26^\circ)
$$
$$
d = \frac{25 \cdot \tan(26^\circ)}{\tan(34^\circ) - \tan(26^\circ)}
$$

Now we can calculate $$ d $$ using the tangent values:
- $$ \tan(34^\circ) \approx 0.6745 $$
- $$ \tan(26^\circ) \approx 0.4877 $$

Substituting these values:
$$
d = \frac{25 \cdot 0.4877}{0.6745 - 0.4877} = \frac{12.1925}{0.1868} \approx 65.1 \text{ m}
$$

Now we can find the height $$ h $$ using equation (1):
$$
h = d \cdot \tan(34^\circ) \approx 65.1 \cdot 0.6745 \approx 43.9 \text{ m}
$$

Thus, the height of the office tower $$ TA $$ is approximately $$ \boxed{43.9} $$ meters.
The height of the office tower is approximately 43.9 meters.

As part of her assignment, Devi has to use her clinometer to measure the height of an
office tower . From a point , she observes that angle . She then walks 25 m
away from the office tower to a point and observes that angle .
Find the height of the sfice tover.

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As part of her assignment, Devi has to use her clinometer to measure the height of an office tower . From a point , she observes that angle . She then walks 25 m away from the office tower to a point and observes that angle . Find the height of the sfice tover.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Trigonometry Questions

As part of her assignment, Devi has to use her clinometer to measure the height of an
office tower . From a point , she observes that angle . She then walks 25 m
away from the office tower to a point and observes that angle .
Find the height of the sfice tover.