Question

find the sine of ∠d.

triangle with right angle at b, sides: bc = √5, bd = √30, cd = √35

write your answer in simplified, rationalized form. do not round.

sin(d) = blank box fraction and square root buttons

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle D$, identify opposite and hypotenuse.

Step2: Identify sides

In $\triangle BCD$ (right-angled at $B$), opposite side to $\angle D$ is $BC = \sqrt{5}$, hypotenuse is $CD = \sqrt{35}$.

Step3: Calculate sine

$\sin(D) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\sqrt{5}}{\sqrt{35}}$

Step4: Rationalize denominator

Simplify $\frac{\sqrt{5}}{\sqrt{35}} = \frac{\sqrt{5}}{\sqrt{5 \times 7}} = \frac{\sqrt{5}}{\sqrt{5} \times \sqrt{7}} = \frac{1}{\sqrt{7}} = \frac{\sqrt{7}}{7}$ (multiply numerator and denominator by $\sqrt{7}$).

Answer:

$\frac{\sqrt{7}}{7}$