Chapter 13: Q46. (page 708)

A geologist measured a $40 °$ angle of elevation to the top of a mountain. After moving 0.5 km farther away the angle of elevation was $34 °$ . How high is the top of the mountain?

Short Answer

Expert verified

The top of the mountain is $1.719 Km$ .

Step by step solution

Step 1. Write down the given information.

It is given that the angle of elevation of the top of a mountain changes from $40 {}^{\circ} to 34 °$ as the geologist moves 0.5 km farther away as shown in diagram below.

Step 2. Calculation.

Apply trigonometric ratios in triangle ABC and triangle ABD. Therefore,

$\begin{matrix} \tan 40 ° = \frac{h}{x} .... (From Δ ABC) \\ h = x \tan 40 ° .... (1) \\ And, \tan 34 ° = \frac{h}{x + 0.5} .... (From Δ ABD) \\ x + 0.5 = \frac{h}{\tan 34 °} \\ x = \frac{h}{\tan 34 °} - 0.5 \end{matrix}$

Plugging $x = \frac{h}{\tan 34 °} - 0.5$ in (1) and simplifying for $(h)$ gives,

$\begin{matrix} h = (\frac{h}{\tan 34 °} - 0.5) \tan 40 ° \\ h = \frac{h \tan 40 °}{\tan 34 °} - 0.5 \tan 40 ° \end{matrix}$

Further simplifying,

$\begin{matrix} (\frac{\tan 40 °}{\tan 34 °} - 1) h = 0.5 \tan 40 ° \\ (\frac{\tan 40 ° - \tan 34 °}{\tan 34 °}) h = 0.5 \tan 40 ° \\ h = \frac{0.5 \tan 40 ° \tan 34 °}{\tan 40 ° - \tan 34 °} \\ h = 1.719 Km \end{matrix}$

Since, the value of $h = 1.719 Km$ . Hence, the top of the mountain is $1.719 Km$ .

Step 3. Conclusion.

The top of the mountain is $1.719 Km$ .

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A geologist measured a $40 °$ angle of elevation to the top of a mountain. After moving 0.5 km farther away the angle of elevation was $34 °$ . How high is the top of the mountain?

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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A geologist measured a 40° angle of elevation to the top of a mountain. After moving 0.5 km farther away the angle of elevation was 34°. How high is the top of the mountain?

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Statistics

Pure Maths

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

A geologist measured a $40 °$ angle of elevation to the top of a mountain. After moving 0.5 km farther away the angle of elevation was $34 °$ . How high is the top of the mountain?