Question

Which triangle is similar to △ABC if sin(A) = One-fourth, cos(A) = StartFraction StartRoot 15 EndRoot Over 4 EndFraction, and tan(A) = StartFraction 1 Over StartRoot 15 EndRoot EndFraction?

Answer 1

D. ΔXYZ

Explanation:

Answer 2

ΔXYZ

Explanation:

Trigonometric identities are equations which are true for right angled triangles. They are:

sin(A) = opposite / hypotenuse, cos(A) = adjacent / hypotenuse, tan(A) = opposite / adjacent.

Given triangle ABC with ∠A with side BC opposite to the angle, ∠B with side AC opposite to the angle, ∠C with side AB opposite to the angle.

sin(A) = opposite / hypotenuse = BC / AC = 1/4

BC = 1, AC = 4

cos(A) = adjacent / hypotenuse = AB / AC = √15 / 4

AB = √15

tan(A) = opposite / adjacent = BC / AB = 1 / √15

Two triangles are said to be similar if the ratio of their corresponding sides are in the same proportion.

ΔXYZ and ΔABC are similar because the ratio of their corresponding sides are in the same proportion.

For adjacent side; XZ / AB = 6√15 / √15 = 6

For opposite side; YZ / BC = 6/1 = 6

For hypotenuse side; XY / AC = 24 / 4 = 6