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Gemiola [76]
2 years ago
9

Felicia wants to build a kite with the shape shown. If AC is 60 cm, how many centimeters are in the length of BD?

Mathematics
1 answer:
Kay [80]2 years ago
6 0

Answer:

Step-by-step explanation:

By applying tangent rule in the given right triangle AOB,

tan(30°) = \frac{\text{Opposite side}}{\text{Adjacent side}}

\frac{1}{\sqrt{3}}=\frac{BO}{OA}

OA=BO(\sqrt{3})

By applying tangent rule in the given right triangle BOC,

tan(60°) = \frac{OC}{BO}

OC = BO(√3)

OA + OC = AC

BO(\sqrt{3})+BO(\sqrt{3}) =60

2√3(BO) = 60

BO = 10√3

OC = BO(√3)

OC = (10√3)(√3)

OC = 30

By applying tangent rule in right triangle DOC,

tan(60°) = \frac{OD}{OC}

OD = OC(√3)

OD = 30√3

Since, BD = BO + OD

BD = 10√3 + 30√3

BD = 40√3

      ≈ 69.3

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