Question

Match the trigonometric ratios with their values based on the triangle shown in the diagram

Answer 1

SOH CAH TOA: sinθ = opp/hyp, cosθ = adj/hyp, tanθ = opp/adj

So we go through all of the values:

sinD = ⁴/₅

sinC = ³/₅

sinD * cosD = ⁴/₅ * ³/₅ = ¹²/₂₅

tanC * tanD = ³/₄ * ⁴/₃ = 1 --> Doesn't match with anything

cosC * tan D = ⁴/₅ * ⁴/₃ = ¹⁶/₁₅

Answer 2

Answer:

The ratios are as follows:

  $\sin D=\dfrac{4}{5}$

  $\sin C=\dfrac{3}{5}$

  $\sin D\times \cos D=\dfrac{12}{25}$

  $\tan C\times \tan D=1$

  $\cos C\times \tan D=\dfrac{16}{15}$

Step-by-step explanation:

The trignometric ratio are defined as follows:

$\sin \theta=\dfrac{opposite\ side}{hypotenuse}$

where opposite side is the side opposite to angle theta

and

$\cos \theta=\dfrac{adjacent\ side}{hypotenuse}$

and adjacent side the side which is adjacent to angle θ and hypotenuse is the hypotenuse of the right angled triangle.

and

$\tan \theta=\dfrac{opposite\ side}{adjacent\ side}$

Hence, from the right angled triangle that is provided to us we have:

$\sin D=\dfrac{4}{5}$

$\sin C=\dfrac{3}{5}$

and $\cos D=\dfrac{3}{5}$

$\cos C=\dfrac{4}{5}$

$\tan C=\dfrac{3}{4}$

and $\tan D=\dfrac{4}{3}$

Hence,

$\sin D\times \cos D=\dfrac{4}{5}\times \dfrac{3}{5}\\\\\\\sin D\times \cos D=\dfrac{12}{25}$

$\tan C\times \tan D=\dfrac{3}{4}\times \dfrac{4}{3}\\\\\\\tan C\times \tan D=1$

and

$\cos C\times \tan D=\dfrac{4}{5}\times \dfrac{4}{3}\\\\\\\cos C\times \tan D=\dfrac{16}{15}$