Question

Question 1

Answer 1

For the answer to the question If the distance from the plane (P) to the tower (T) is 5,000 ft., how far is the bird (B) from the plane (P)? The answer is 11,779 feet.
And for the answer to the second question on what is the angle of depression from the bird (B) to the observer (O)? The answer is 56.31°

Answer 2

Answer:

Q1. 12,788 feet

Q2. 41,81 °

Q3. 25,636 feet

Q4. 224 feet

Q5. 12,287 feet

Step-by-step explanation:

Before reading ignore the Â.

We can solve most of those problems using the function sine and $sine^{-1}$. It goes as following:

Q1.

We know that $sin(23o) \approx 0.39$ so we can use the following expression to find x:

$sin(39o) = \frac{ca}{x}$

Where ca is the vertical line from the ground and the plane. in this case ca = 5000.

$0.39 = \frac{5000}{x} \Rightarrow \ 0.39x = 5000 \Rightarrow x \approx 12788$

Q2.

Now we want to find the angle between the lines. But the same principle applies here.

$sin(\theta) = \frac{6000}{9000} = \frac{2}{3}$

We can apply the inverse function $sine^{-1}$ to solve for $\theta$.

$sin^{-1}[sin(\theta)] = sin^{-1}(\frac{2}{3}) \Rightarrow \theta = sin^{-1}(\frac{2}{3}) = 41,81$

Q3.

We use the same principle of Q1 in this one. Also we know that $sin(55o) = 0.819$

$sin(55o) = \frac{21000}{x} \Rightarrow 0.819 = \frac{21000}{x} \Rightarrow x = 25636$

Q4.

We know that both sides of the pyramid are equal when separated by the height. So we can say that base = 2x. We just need to find x, that can be found in the same way we found before. This time with the tangent function.

$tan(62o) = 1.8807$

$1.8807 = \frac{211}{x} \Rightarrow x \approx 112 \Rightarrow base \approx 2*112 = 224$

Q5.

We use the sine function here once again.

$sin(55o) = 0.819 = \frac{x}{15000} \Rightarrow x \approx 12287$