Question

Find the indicated angles round your final answer to the nearest hundredths! Show all work!

Answer 1

Explanation:

the 3 main tools we need here :

- the sum of all angles in a triangle is always 180°.

- Pythagoras : c² = a² + b²

- the law is sine : a/sin(A) = b/sin(B) = c/sin(C)

b)

in order to be able to use the law of sine, we need to get the length of the baseline.

Pythagoras

baseline² = 8² + 5² = 64 + 25 = 89

baseline = sqrt(89)

8/sin(angle) = sqrt(89)/sin(90) = sqrt(89)/1 = sqrt(89)

sin(angle) = 8/ sqrt(89) = 0.847998304...

angle = 57.99461679...° ≈ 58° (or 57.99° officially rounded to the nearest hundredths)

c)

7/sin(x) = 12/sin(90) = 12/1 = 12

sin(x) = 7/12 = 0.583333333...

x = 35.68533471...° ≈ 35.69°

y = 180 - 90 - 35.69 = 54.31°

d)

9² = RG² + 7.5²

81 = RG² + 56.25

RG² = 24.75

RG = sqrt(24.75) = 4.974937186...

sqrt(24.75)/sin(T) = 9/sin(90) = 9/1 = 9

sin(T) = sqrt(24.75)/9 = 0.552770798...

T = 33.55730976...° ≈ 33.56°

Answer 2

given and explained below.

Explanation:

b)

opposite/ adjacent = tan(∅)

tan(∅) = 8 /5

∅ =
`tan^(-1)( 8/5)`

∅ = 58.99°

c)

opposite/hypotenuse = sin(x)

sin(x) = 7 / 12

x =
`sin^(-1) (7/12)`

x = 35.68°

adjacent/hypotenuse = cos(y)

cos(y) = 7/12

y=
`cos^(-1) (7/12)`

y = 54.31°

d)

cos(T) = adjacent / hypotenuse

cos(T) = 7.5/9

T =
`cos^(-1)(7.5 / 9)`

∠T=33.56°