Question

find h as indicated in the figure. h= (round to the nearest integer as needed.) question 5, 2.5.35 hw score: 33.33%, 2 of 6 points points: 0 of 1

Explanation:

Step1: Analyze the triangle

We have a triangle with two angles \(24.4^\circ\) and \(50.7^\circ\), and the side adjacent to the difference of these angles is 490. First, find the difference in angles: \(50.7^\circ - 24.4^\circ = 26.3^\circ\). Let the base of the smaller triangle be \(x\) and the base of the larger triangle be \(y\). Then \(y - x = 490\). Also, \(h = x\tan(50.7^\circ)\) and \(h = y\tan(24.4^\circ)\). So \(x\tan(50.7^\circ) = (x + 490)\tan(24.4^\circ)\).

Step2: Solve for \(x\)

Expand the equation: \(x\tan(50.7^\circ) = x\tan(24.4^\circ) + 490\tan(24.4^\circ)\)
Subtract \(x\tan(24.4^\circ)\) from both sides: \(x(\tan(50.7^\circ) - \tan(24.4^\circ)) = 490\tan(24.4^\circ)\)
Calculate \(\tan(50.7^\circ) \approx 1.227\), \(\tan(24.4^\circ) \approx 0.453\)
So \(x(1.227 - 0.453) = 490\times0.453\)
\(x\times0.774 = 221.97\)
\(x = \frac{221.97}{0.774} \approx 286.8\)

Step3: Find \(h\)

Now, \(h = x\tan(50.7^\circ)\)
\(h \approx 286.8\times1.227 \approx 352.0\) (Rounded to nearest integer)

Answer:

\(352\)