Question

With steps please

A student uses a clinometer to measure the angle of elevation of a sign that marks the point on a tower that is 45 m above the ground. The angle of elevation is 32° and the student holds the clinometer 1.3 m above the ground. He then measures the angle of elevation of the top of the tower as 47º. Sketch and label a diagram to represent the information in the problem. Determine the height of the tower to the nearest tenth of a metre​

Answer 1

Answer:
`75\ m`

Explanation:

Given

The tower is 45 m high and Clinometer is set at 1.3 m above the ground

From the figure, we can write

`\Rightarrow \tan 32^(\circ)=(43.7)/(x)\\\\\Rightarrow x=(43.7)/(\tan 32^(\circ))\\\\\Rightarrow x=69.93\ m`

Similarly, for
`\triangle ACD`

`\Rightarrow \tan 47^(\circ)=(43.7+y)/(x)\\\\\Rightarrow 69.93* \tan 47^(\circ)=43.7+y\\\\\Rightarrow 74.99=43.7+y\\\Rightarrow y=31.29\ m`

Height of the tower is
`43.7+31.29\approx 75\ m`