Question

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. B = 51.7°, a = 28.1 ft

Accepted Answer

Identify the given elements of the right triangle: angle $$ B = 51.7^\circ $$, side $$ a = 28.1  ft$$, and the right angle $$ C = 90^\circ . $$Recall that side $$ a  is $$opposite angle $$ A $$, side $$ b  is $$opposite angle $$ B $$, and side $$ c  is $$the hypotenuse opposite the right angle $$ C . $$Calculate angle $$ A $$ using the fact that the sum of angles in a triangle is $$ 180^\circ . $$Since $$ C = 90^\circ $$, use the formula: $$ A = 90^\circ - B . $$Use the Law of Sines to find the hypotenuse $$ c . $$The Law of Sines states: $$ \frac{a}{\sin A} = \frac{c}{\sin C} . $$Since $$ C = 90^\circ $$, $$ \sin C = 1 $$, so $$ c = \frac{a}{\sin A} . $$Find side $$ b $$ using the Law of Sines again or by using the Pythagorean theorem. Using Law of Sines: $$ b = c 	imes \sin B . $$Alternatively, use $$ b = \sqrt{c^2 - a^2} . $$Express all answers with the correct units and in decimal degrees as given. Since the angle $$ B $$ was given in decimal degrees, keep angles $$ A $$ and $$ B  in $$decimal degrees, and sides in feet.

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주요 개념

Right Triangle Properties

Trigonometric Ratios (Sine, Cosine, Tangent)

Angle Measurement and Conversion