Question

In 4BCD, the measure of _D=90°, CB = 25, BD = 7, and DC = 24. What is the value of the sine of ZC to the nearest hundredth?

Answer 1

Using the sine rule,

`\frac{\sin\text{ C}}{c}\text{ = }\frac{\sin \text{ D}}{d}`

From the sketch,

D =90 d=25 c = 7

substitute the values into the formula

`\frac{\sin\text{ C}}{7}=(\sin 90)/(25)`

cross-multiply

`25\text{ sin C = 7 sin90}`
`25\text{ sin C=7}*1`

Divide both-side of the equation by 25

`\sin C=(7)/(25)`
`\sin \text{ C = 0.28}`