Ineed to find the measure of each angle indicated. with number 17 and 18!

17) Ф = 57.99 ≅ 58°

18) Ф = 20.10 ≅ 21°

Step-by-step explanation:

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Now lets solve the problems

17) In Δ ACB

∵ m∠C = 90°

∵ BC = 16 units ⇒ opposite to angle Ф

∵ AC = 10 units ⇒ adjacent to angle Ф

∵ tanФ = opposite/adjacent

∴ tanФ = BC/AC

∴ tanФ = 16/10 = 8/5

- To find angle Ф find the inverse of tan (tan^-1)

∴ Ф = tan^-1 8/5 = 57.99 ≅ 58°

18) In Δ ACB

∵ m∠C = 90°

∵ BC = 5.6 units ⇒ opposite to angle Ф

∵ AC = 15.3 units ⇒ adjacent to angle Ф

∵ tanФ = opposite/adjacent

∴ tanФ = BC/AC

∴ tanФ = 5.6/15.3 = 56/153

- To find angle Ф find the inverse of tan (tan^-1)

∴ Ф = tan^-1 56/153 = 20.10 ≅ 21°

17).  θ = 57.99°

18).  θ =20.10°

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

Question (17).

From the figure we can write,

Tan θ = Opposite side/Adjacent side

= BC/AC = 16/10 = 1.6

θ = Tan⁻¹ (1.6) = 57.99°

Question 18)

From the figure we can write,

Tan θ = Opposite side/Adjacent side

= BC/AC = 5.6/15.3 = 0.366

θ = Tan⁻¹ (0.366) = 20.10°

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