Question

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

Answer 1

`\approx 150 \: ft`

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) ) = (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

Answer 2

height : 150 feet

Explanation:

`\sf \sf tan(x)= (opposite)/(adjacent)`

using tan rule:

`\hookrightarrow \sf tan(62)= (b)/(80)`

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

`\hookrightarrow \sf b =150.46 \ feet`