1. ## Trig help

The angle of elevation to a building is 30 degrees. From a point 20 m directly toward the building, the angle of elevation changes to 40 degrees. Find the height of the building. Include a diagram in your solution.

Do I make 3 triangles for this question?

2. Originally Posted by sinjid9
The angle of elevation to a building is 30 degrees. From a point 20 m directly toward the building, the angle of elevation changes to 40 degrees. Find the height of the building. Include a diagram in your solution.

Do I make 3 triangles for this question?
Draw a horizontal line representing the ground. On the left draw a vertical line and on the right put a point 5 inches away from the vertical line.

label the distance 20m.

Now you have an angle and distance.

$cos(\theta)=\frac{adj}{hyp}\rightarrow cos(30)=\frac{20}{r}$

$cos(\theta)=\frac{adj}{hyp}\rightarrow cos(40)=\frac{20}{r}$

The length you want is y $r^2=x^2+y^2$

3. Hello, sinjid9!

The angle of elevation to a building is 30°.
From a point 20 m closer to the building, the angle of elevation is 40°.
Find the height of the building. Include a diagram in your solution.
Code:
    A o
|  *  *
|     *     *
h |        *        *
|           *           *
|          40° *        30°   *
B o - - - - - - - - o - - - - - - - - o
x        D       20        C

The building is: $h \,=\,AB.$
$\angle ACB = 30^o,\;\angle ADB \,=\,40^o,\;DC \,=\,20$
Let $x \,=\,BD.$

In right triangle $ABC\!:\;\;\tan30 \:=\:\frac{h}{x+20} \quad\Rightarrow\quad x \:=\:\frac{h-20\tan30}{\tan30}$ .[1]

In right triangle $ABD\!:\;\;\tan40 \:=\:\frac{h}{x} \quad\Rightarrow\quad x \:=\:\frac{h}{\tan40}$ .[2]

Equate [1] and [2]: . $\frac{h-20\tan30}{\tan30} \;=\;\frac{h}{\tan40} \quad\Rightarrow\quad h\tan40 - 20\tan30\tan40 \;=\;h\tan30$

. . . . . . . . $h\tan40 - h\tan30 \:=\:20\tan30\tan40 \quad\Rightarrow\quad h(\tan40-\tan30) \:=\:20\tan30\tan40$

Therefore: . $h \;=\;\frac{20\tan30\tan40}{\tan40-\tan30} \;=\;37.01666314 \;\approx\;37\text{ m}$

4. I was thinking of rotating the line from the ground not from the wall.