Question

Find the height of the building to the nearest foot in the diagram below. Show work.

Answer 1

Answer:

height : 150 feet

Step-by-step explanation:

$\sf \sf tan(x)= \dfrac{opposite}{adjacent}$

using tan rule:

$\hookrightarrow \sf tan(62)= \dfrac{b}{80}$

$\hookrightarrow \sf b = tan(62)*80$

$\hookrightarrow \sf b =150.46 \ feet$

Answer 2

Answer:

$\approx 150 \: ft$

Step-by-step explanation:

recall sohcahtoa

• sin(x)=opposite/hypotenuse
• cos(x)=adjacent/hypotenuse
• tan(x)=opposite/adjacent

here,

• The adjacent side is 80 ft
• x°=62°
• The opposite side is the height

To find:

• The opposite side or the height

since we are given the value of adjacent side and need to figure out the opposite side , we will work with tan function,

So,

$\tan( {62}^{ \circ} ) = \dfrac{h}{80}$

$\implies \: h = 80\tan( {62}^{ \circ} )$

using calculator,we acquire

$\implies \: h \approx 150 \: ft$

hence, the height of the building is approximately 150ft