Question

What is the answer to this question.

\angle DAC=\angle BAD∠DAC=∠BADangle, D, A, C, equals, angle, B, A, D.
What is the length of \overline{BD}
BD
start overline, B, D, end overline?
Round to one decimal place.

Answer 1

3.6

Explanation:

5.7/x=5.1/3.2

Answer 2

3.6

Explanation:

It can be seen from the diagram that ΔDAC and ΔABD are right angled triangle.

Using the SOH, CAH, TOA trigonometry identity on ΔDAC where;

AC is the hypotenuse = 5.1

CD is the opposite (since it faces the angle directly)

According to SOH;

Sin
`\theta` = opp/hyp

sin
`\theta = (3.2)/(5.1)`

`sin\theta = 0.6275\\\theta = sin^(-1) 0.6275\\\theta = 38.9^(0)`

∠DAC = ∠BAD = 38.9°

According to ΔABD, the opposite side is DB which is unknown and the hypotenuse id AB i.e 5.7

Using SOH;

`sin BAD = opp/hyp\\sin \theta = BD/AB\\sin 38.9^(0) = BD/5.7\\BD = 5.7 sin 38.9^(0)\\BD = 3.58\\`

BD ≈ 3.6 to one dp