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mihalych1998 [28]
1 year ago
10

Find the number of distinct triangles with the measurements a = 8, b = 14, and A = 30°.​

Mathematics
1 answer:
Maslowich1 year ago
5 0

Answer: 2

Step-by-step explanation:

By the law of sines,

\frac{\sin B}{b}=\frac{\sin A}{a} \\ \\ \frac{\sin B}{14}=\frac{\sin 30^{\circ}}{8} \\ \\ \frac{\sin B}{14}=\frac{1}{16} \\ \\ \sin B=\frac{14}{16} \\ \\ B=\sin^{-1} \left(\frac{14}{16} \right), 180^{\circ}-\sin^{-1} \left(\frac{14}{16} \right) \\ \\ B \approx 61.04^{\circ}, 118.96^{\circ}

Since either of these values for B will form a triangle (as A+B will be less than 180 degrees), 2 triangles can be formed with these measurements.

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3
ValentinkaMS [17]

Answer:

P = 58

Step-by-step explanation:

<em>The image if the circle and triangle can be found online</em>

Given

JA = 8

AL = 8

CK = 10

Required

The perimeter of JKL

Since the mid-points of the tangents are A, B and C respectively.

JK = JB + BK

Where

JB = JA = 8

BK = CK = 10

So:

JK =8+10 =18

JL = JA + AL

JL = 8+11 = 19

KL = CL + CK

Where

CL  =AL = 11

So:

KL = 11+10 = 21

So, the perimeter (P) is:

P = JK+ KL +JL

P = 18 + 19 + 21

P = 58

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