Question

Need Help ASAP!!.

1. Error Analysis: Anita Help drew the triangle below. Her friend, Greta Life, told her that her triangle was incorrect. Who is correct? Explain.

2. The Geo Air pilot is looking at SCCA from the plane. From the aircraft the angle of depression is 17 degrees. If the plane is at an altitude of 10,000 feet, approximately how far is the plane to SCCA? Round your answer to the nearest tenth. The image is not drawn to scale.

3. Trey Rigg’s house is next to a large pine tree. The National Weather Center has issued a warning for high winds. Trey is worried that his house is at risk of being crushed by the pine tree. Trey’s house is 25 feet from the base of the tree and Trey calculates the angle of elevation to be 43 degrees from the base of his house. Find the height of the tree to determine if Trey’s house is at risk. Round your answer to the nearest tenth.

Picture 1 is for Number 1.
Picture 2 is for Number 2.
Picture 3 is for Number 3.

Answer 1

Part 1) Greta's right, the triangle is incorrect.

Part 2)
`34,203\ ft`

Part 3) The height of the tree is
`23.3\ ft`, Trey’s house is not at risk

Explanation:

Part 1) we know that

In the right triangle of the figure

`sin(30\°)=(1)/(2)`

`sin(30\°)=(6√(3))/(12)=(√(3))/(2)`

Compare

`(1)/(2)\\eq(√(3))/(2)`

therefore

The triangle is not correct

Because

The side adjacent to the 30 degree angle should be
`6√(3)` and the side opposite the 30 degree angle should be
`6`

Part 2)

Let

x--------> the distance from the airplane to the SCCA (hypotenuse of the right triangle)

we know that

`sin(17\°)=(10,000)/(x)`

`x=(10,000)/(sin(17\°))`

`x=34,203\ ft`

Part 3)

Let

x--------> the height of the tree

we know that

`tan(43\°)=(h)/(25)`

`h=tan(43\°)(25)=23.3\ ft`

`23.3\ ft< 25\ ft`

therefore

Trey’s house is not at risk