Question

complete the steps to determine how many triangles abc can exist with the given measures.
( b = 18.7 ), ( c = 16.1 ) and ( c = 35 ^ { circ } )
what is the approximate value of the height, ( h ), of the triangle? round to the nearest tenth.

Explanation:

Step1: Use the formula for height in a triangle

The formula for the height \(h\) of a triangle with side \(b\) and angle \(C\) is \(h = b\sin C\).

Step2: Substitute the given values

Given \(b = 18.7\) and \(C=35^{\circ}\), we substitute into the formula: \(h = 18.7\times\sin(35^{\circ})\).
Since \(\sin(35^{\circ})\approx0.5736\), then \(h = 18.7\times0.5736\).

Step3: Calculate the value

\(h=18.7\times0.5736 = 10.72632\approx10.7\) (rounded to the nearest tenth).

Answer:

\(10.7\)