Question

Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46.

Accepted Answer

Identify the given information in the right triangle, such as the lengths of sides or measures of angles. Typically, you will have one right angle (90°) and either one other angle or some side lengths provided. Use the Pythagorean theorem to find the missing side if two sides are known. The theorem states: $$a^2$$ + $$b^2$$ = $$c^2$$, where $$c is $$the hypotenuse and $$a$$, $$b$$ are the legs of the triangle. Apply trigonometric ratios (sine, cosine, tangent) to find the unknown angles or sides. For example, if you know an angle $$	heta$$ and a side, use $$\sin(	heta) = \frac{	ext{opposite}}{	ext{hypotenuse}}$$, $$\cos(	heta) = \frac{	ext{adjacent}}{	ext{hypotenuse}}$$, or $$	an(	heta) = \frac{	ext{opposite}}{	ext{adjacent}}. To $$find an angle to the nearest minute, first calculate the angle in decimal degrees using inverse trigonometric functions (e.g., $$\sin$$^{-1}$$, $$\$$cos^{-1}$$, $$	an$$^{-1}$$), then convert the decimal part of the degree to minutes by multiplying by 60. Label the triangle as $$	riangle ABC$$ according to the problem instructions, ensuring that angle C$ is the right angle if specified, and assign sides opposite to each angle accordingly. This helps keep track of which sides correspond to which angles when applying trigonometric ratios.

Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46.

Risposta video verificata per un problema simile:

Concetti chiave

Right Triangle Properties

Trigonometric Ratios (Sine, Cosine, Tangent)

Angle Measurement and Conversion to Minutes