Question

A man is standing on the level ground at a distance of 38.5m from a 40m high tower. He observes the angle of elevation on the top of the tower as 45°. How tall is he

Answer 1

Given data:

The height of the tower is $\mathsf{40}$ m

The distance of the man from the tower is $\mathsf{38.5}$ m

The angle of elevation is $\mathsf{45^{\circ}}$

To find:

The height of the man

Step-by-step explanation:

[First draw the attached diagram and then proceed with the written solution.]

Let, $\mathsf{AB}$ be the tower and $\mathsf{CD}$ be the man. Then $\mathsf{\angle ACE}$ is the angle of elevation.

Draw the line $\mathsf{CE}$ whose length is $\mathsf{38.5}$ m, since $\mathsf{BD=CE}$.

Let, $\mathsf{CD=x}$ m. Then $\mathsf{BE=CD=x}$ m.

So $\mathsf{AE=AB-BE=40-x}$ m.

Since $\mathsf{\Delta AEC}$ is a right-angled triangle,

$\quad \mathsf{\dfrac{AE}{CE}=tan(\angle ACE)}$

$\Rightarrow \mathsf{\dfrac{40-x}{38.5}=tan45^{\circ}=1}$

$\Rightarrow \mathsf{40-x=38.5}$

$\Rightarrow \mathsf{x=40-38.5}$

$\Rightarrow \mathsf{x=1.5}$

Answer: The man is 1.5 m tall.

Read more on Brainly.in

Two towers are in front of each other, and their heights are 25 m and 10 m. The distance between them is 15 m. What angle does the line joining their tops make with the ground?

https://brainly.in/question/29424852