Question

find the unknown measures. round lengths to the nearest hundredth and angle measures to the nearest degree.

Answer 1

Angle I = 44

Measure GH=7.64

Measure GI=7.91

Explanation:

Angle I:

Since we know that m∠H = 46 and m∠G=90, we can find measure angle I by subtracting from 180.

`180=46+90+x\\44=x`

Measure GH:

Since we are given that m∠H = 46, and the triangle is right, we can use trigonometric functions to find the two sides.

First is GH, since it's adjacent to the angle, we will use cosine.

`cos(x)=(adjacent)/(hypotenuse) \\cos(46)=(adjacent)/(11)\\ 11*cos(46)=adjacent\\7.64=adjacent`

Measure GI:

The same idea as previous, only instead we will use sine since we need to find the opposite.

`sin(x) = (opposite)/(hypotenuse)\\ sin(46)=(opposite)/(11)\\ 11*sin(46)=opposite\\7.91 = opposite`