Question

I will give you 100 points HELp

Answer 1

Answer:

CD = 26.0 cm (3 sf)

Step-by-step explanation:

Sine Rule for side lengths

$\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Find length BD:

$\implies \sf \dfrac{AB}{\sin ADB}=\dfrac{BD}{\sin BAD}$

$\implies \sf \dfrac{12}{\sin 35^{\circ}}=\dfrac{BD}{\sin 90^{\circ}}$

$\implies \sf BD=\dfrac{12\sin 90^{\circ}}{\sin 35^{\circ}}$

$\implies \sf BD=20.92136155...cm$

Find length CD:

$\implies \sf \dfrac{BD}{\sin BCD}=\dfrac{CD}{\sin DBC}$

$\implies \sf \dfrac{20.921...}{\sin 52^{\circ}}=\dfrac{CD}{\sin 102^{\circ}}$

$\implies \sf CD=\dfrac{20.921...\sin 102^{\circ}}{\sin 52^{\circ}}$

$\implies \sf CD=25.96941667...cm$

Therefore, CD = 26.0 cm (3 sf)

Answer 2

Answer:

CD ≈ 26.0 cm

Step-by-step explanation:

using the sine ratio in right triangle ABD

sin35° = $\frac{opposite}{hypotenuse}$ = $\frac{AB}{BD}$ = $\frac{12}{BD}$ ( multiply both sides by BD )

BD × sin35° = 12 ( divide both sides by sin35° )

BD = $\frac{12}{sin35}$ ≈ 20.92 cm

using the sine rule in Δ BCD

$\frac{BD}{sinC}$ = $\frac{CD}{sinB}$ , that is

$\frac{20.92}{sin52}$ = $\frac{CD}{sin102}$ ( cross- multiply )

CD × sin52° = 20.92 × sin102° ( divide both sides by sin52° )

CD = $\frac{20.92sin102}{sin52}$ ≈ 26.0 cm ( to 3 significant figures )