Question

solve the right triangle using the given information. a = 75.8 yd, b = 42.9 yd c = □ yd (simplify your answer. type an integer or a decimal. round to the nearest tenth if needed.) a = □°□ (simplify your answers. type integers. round to the nearest ten minutes if needed.) b = □°□ (simplify your answers. type integers. round to the nearest ten minutes if needed.)

Explanation:

Step1: Find side c using Pythagorean theorem

$c=\sqrt{a^{2}+b^{2}}=\sqrt{75.8^{2}+42.9^{2}}=\sqrt{5745.64 + 1840.41}=\sqrt{7586.05}\approx87.1$

Step2: Find angle A using tangent function

$\tan(A)=\frac{a}{b}=\frac{75.8}{42.9}\approx1.767$
$A = \arctan(1.767)\approx60.5^{\circ}$
Converting $0.5^{\circ}$ to minutes: $0.5\times60 = 30'$, so $A = 60^{\circ}30'$

Step3: Find angle B

Since the sum of angles in a triangle is $180^{\circ}$ and it's a right - triangle ($90^{\circ}$), $B=90^{\circ}-A$
$B = 90^{\circ}-60^{\circ}30'=29^{\circ}30'$

Answer:

$c = 87.1$ yd
$A = 60^{\circ}30'$
$B = 29^{\circ}30'$