Question

Need help with this trigonometry word problem

Answer 1

Answer:

$\huge \boxed{ \boxed{ 50 \sqrt{3} \: or \: 86.6}}$

Step-by-step explanation:

to understand this

you need to know about:

• trigonometry
• PEMDAS

let's solve:

to find the height we need to use tan function because we are given adjacent and angle and we need to figure out opposite (height) $\tan(\theta)=\dfrac{opposite}{adjacent}$

let opposite be AC

let adjacent be BC

according to the question:

$\quad \: \tan( {60}^{ \circ} ) = \dfrac{AC}{BC}$

now we need a little bit algebra to figure out AC (height)

1. $\sf \: substitute \: the \: given\: value \: of \: BC : \\ \tan( {60}^{ \circ} ) = \frac{AC}{50}$
2. $\sf sustitute \: the \: value \: of \: \tan( {60}^{ \circ} ) \: i.e \: \sqrt{3} : \\ \sqrt{3 } = \frac{AC }{50}$
3. $\sf cross \: multiplication: \\ 50 \sqrt{3} = AC$
4. $\sf swap \: sides \: (your \: wil) : \\ AC = 50 \sqrt{3} \\AC = 86.6 \: ( \sf \: decimal \: if\: needed)$

$\text{we are done!}$

Answer 2

Answer:

86.6

Step-by-step explanation:



Here, AB represents height of the building, BC represents distance of the building from the point of observation.

In the right triangle ABC, the side which is opposite to the angle 60 degree is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse side (AC) and the remaining side is called adjacent side (BC).

Now we need to find the length of the side AB.

tanθ  =  Opposite side/Adjacent side

tan 60°  =  AB/BC

√3  =  AB/50

√3 x 50  =  AB

AB  =  50√3

Approximate value of √3 is 1.732

AB  =  50 (1.732)

     AB  =  86.6 m

So, the height of the building is 86.6 m