A) Given: Lateral area = 156 SK = 10, Find: m∠KSM

m∠KSM = 59.55°

Step-by-step explanation:

The formula of the lateral area of a cone is LA = Cl, where c is the circumference of the base and l is the slant height

The formula of the circumference of a circle is C = 2πr

From the figure

SO is the height of the cone

KM is the diameter of the base

SO⊥ KM

SK and SM are slant heights

We can use the trigonometry ratio in triangle SOK to find angle KSO, then multiply its measure by 2 to find the measure of ∠KSM, because m∠KSO is equal to m∠MSO

∵ LA =   Cl

∵ C = 2πr

∴ LA = (2πr) l

∴ LA = πrl

∵ LA = 156

- l is the side SK

∵ SK = 10 units

∴ l = 10

- Substitute the values of LA and l in the formula above

∵ 156 = 10πr

- Divide both sides by 10π

∴ = r

∴ r =

∵ sin(∠KSO) =

∵ OK is the radius of the base

∴ sin(∠KSO) =

∴ sin(∠KSO) =

- Use to find m∠KSO

∴ ∠KSO =

∴ ∠KSO = 29.77°

∵ m∠KSO = m∠MSO

∴ m∠KSM = 2 m∠KSO

∴ m∠KSM = 2(29.77°)

∴ m∠KSM = 59.55°

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step-by-step explanation: