Solver for x. Round to the nearest tenth. (Show Work)

Answer/Step-by-step explanation:

Recall: SOHCAHTOA

2. Reference angle = 62°

Adjacent = 25

Opposite = x

Apply TOA:

Tan 62 = Opp/Adj

Tan 62 = x/25

25*Tan 62 = x

x ≈ 47.0 (nearest tenth)

3. Reference angle = 26°

Hypotenuse = x

Opposite = 11

Apply SOH:

Sin 26 = Opp/Hyp

Sin 26 = 11/x

x × Sin 26 = 11

x = 11/Sin 26

x ≈ 25.1 (nearest tenth)

4. Reference angle = 48°

Hypotenuse = 32

Opposite = x

Apply SOH:

Sin 48 = Opp/Hyp

Sin 48 = x/32

32 × Sin 48 = x

x ≈ 23.8 (nearest tenth)

5. Reference angle = 12°

Hypotenuse = x

Adjacent = 29

Apply CAH:

Cos 12 = Adj/Hyp

Cos 12 = x/29

29 × Cos 12 = x

x ≈ 28.4 (nearest tenth)

6. Reference angle = x

Hypotenuse = 15

Adjacent = 14

Apply CAH:

Cos x = Adj/Hyp

Cos x = 14/15

x = cos^{-1}(14/15)

x ≈ 21.0° (nearest tenth)

7. Reference angle = x

Opposite = 19

Adjacent = 23

Apply TOA:

Tan x = Opp/Adj

Tan x = 19/23

x = Tan^{-1}(19/23)

x ≈ 39.6° (nearest tenth)

8. Reference angle = x

Hypotenuse = 17

Adjacent = 9

Apply CAH:

Cos x = Adj/Hyp

Cos x = 9/17

x = Cos^{-1}(9/17)

x ≈ 58.0° (nearest tenth)

9. Reference angle = x

Hypotenuse = 45

Opposite = 43

Apply SOH:

Sin x = Opp/Hyp

Sin x = 43/45

x = Sin^{-1}(43/45)

x ≈ 72.9° (nearest tenth)

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32