Question

ΔABC is a right triangle in which ∠B is a right angle, AB = 1, AC = 2, and BC = sqrt(3).

cos C × sin A =

I think the answer is 3/4, because cos(c) = adj / hypot and sin(a) = opposite / hypot

cos(c) = sqrt(3) / 2
sin(a) = sqrt(3) / 2
which is 3/4 when multiplied.

Answer 1

`(3)/(4)`

Explanation:

cosC = cos30° =
`(adjacent)/(hypotenuse)` =
`(BC)/(AC)` =
`(√(3) )/(2)`

sinA = sin60° = cos30° =
`(√(3) )/(2)`

Hence

cosC × sinA =
`(√(3) )/(2)` ×
`(√(3) )/(2)` =
`(3)/(4)`

Answer 2

`(3)/(4)`

Explanation:

Since,

`\sin \theta=\frac{Opposite leg of }\theta}{\text{Hypotenuse}}`

`\cos \theta=\frac{Adjacent leg of }\theta}{\text{Hypotenuse}}`

Given,

In triangle ABC,

AB = 1 unit, AC = 2 unit, and BC = √3 unit

Thus, by the above formule,

`\cos C = (√(3))/(2)`

`\sin A=(√(3))/(2)`

`\implies \cos C* \sin A =  (√(3))/(2)* (√(3))/(2)= (3)/(4)`