Question

A surveyor takes measurements of a cliff from across a river as shown. What is the height, h, of

the cliff?

Answer 1

Check the picture below.

`\sin( 47^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{52}} \implies 52\sin(47^o)=z \implies 38.03\approx z \\\\[-0.35em] ~\dotfill\\\\ \tan(62^o )=\cfrac{\stackrel{opposite}{h}}{\underset{adjacent}{38.03}} \implies 38.03\tan(62^o)=h \implies 72\approx h`

Make sure your calculator is in Degree mode.

Answer 2

Height= 71.47

Explanation:

Remember Some People Have Curly Brown Hair Trough Proper Brushing.

Which represents Sin∅ = p/h, Cos∅ = b/h, Tan∅= p/b.

The letters stand for:

h- hypotenuse which is the side opposite to the right angle.

b- The side which has two angles.

p- The other side which is between the hypotenuse and base here unknown.

I will label everything in the triangle for you to understand.

We can find the angle by constructing an equation using the trigonometric ratio as you can see in triangle 1, the base is unknown let it be x and the hypotenuse is given which is 52°

So as mentioned earlier, CosA = b/h

Cos 47°= x/52

Rearrange:

x= 52Cos47° (cross multiplication)

x=35.4639... m

Now in triangle 2, you have to find the base but no data is given so we can use the Pythogerous theorem.

h²= p²+b²

p²= h²-b²

p²= 52²-35.463...²

p= √1446.310753

p= 38

So now we got the base of triangle 2 and we can use the trigonometric ratio to find h (perpendicular).

TanB= p/b

Tan 62°= h/38

h= 38Tan 62°

h= 71.47 m