Question

elevation and depression in mathematics. Questions in images. Thanks!

Answer 1

Answer:

1) 29.2 feet ( approx)

2) 45988.6 feet.

Step-by-step explanation:

1) By the given diagram,

We can write,

$tan 22^{\circ} = \frac{x}{60}$

$\implies x = 60\times tan22^{\circ} = 24.2415735501\approx 24.2$

Thus, the height of the barn from the ground = 24.2 + 5 = 29.2 feet ( Approx)

2) By the Alternative interior angle theorem,

The angle of elevation in this situation ( shown in the below diagram ) must be same as angle of depression and equals to 4°,

Hence, we can write,

$sin4^{\circ}=\frac{3208}{x}$

$x = \frac{3208}{sin4^{\circ}}=45988.5631801\approx 45988.6$

Thus, the plane is approximately 45988.6 feet away.

Answer 2

QUESTION 1

Let us determine the value of $x$ first.

Using the tangent ratio;

$\tan(22\degree)=\frac{x}{60}$

$\Rightarrow x=60\tan(22\degree)$

$\Rightarrow x=24.2ft$

The height of the barn from the ground is $5+24.2=29.2ft$ to the nearest tenth.

QUESTION 2

We use the alternate interior angle property to obtain one of acute angles of the triangle to be $4\degree$. See diagram.

We now use the sine ratio to get;

$\sin(4\degree)=\frac{3208}{x}$

This implies that;

$x=\frac{3208}{\sin(4\degree)}$

We simplify to get;

$x=45988.56$

The airplane is about 45988.6 feet away.