Question

Find The Missing Side. Round to the Nearest Tenth.

Answer 1

Explanation:

1). From the triangle given in the figure,

m∠BAD = 26°

By applying tangent rule in ΔADB,

tan(∠BAD) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

tan(26°) =
`(BD)/(AD)`

BD = 21[tan(26°)]

BD = 10.24

By applying sine rule in ΔBDC,

sin(52°) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

sin(52°) =
`(10.24)/(x)`

x =
`\frac{10.24}{\text{sin}(52)}`

x = 12.99

x ≈ 13.0 units

2). By applying cosine rule in ΔADB,

cos(39°) =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

cos(39°) =
`(BD)/(50)`

BD = 50cos(39°)

BD = 38.86

By applying sine rule in ΔBDC,

sin(24°) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

sin(24°) =
`(38.86)/(x)`

x =
`\frac{38.86}{\text{sin(24)}}`

x = 95.54

x ≈ 95.5 units