Finding Missing Sides and Angles Right Triangle Trig Review

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: $$c^2 = a^2 + b^2$$ .

To find the length of a missing side in a right triangle, you can use the Pythagorean theorem if you know the lengths of the other two sides. If you know one side and an angle, you can use trigonometric ratios (sine, cosine, tangent) to find the missing side.

The sine ratio is defined as the ratio of the length of the opposite side (O) to the length of the hypotenuse (H). It can be expressed as: $$\text{sine} = \frac{O}{H}$$ .

The cosine ratio is defined as the ratio of the length of the adjacent side (A) to the length of the hypotenuse (H). It can be expressed as: $$\text{cosine} = \frac{A}{H}$$ .

The tangent ratio is defined as the ratio of the length of the opposite side (O) to the length of the adjacent side (A). It can be expressed as: $$\text{tangent} = \frac{O}{A}$$ .

To calculate an angle in a right triangle, you can use the inverse trigonometric functions: \( \text{angle} = \sin^{-1}(\frac{O}{H}), \text{angle} = \cos^{-1}(\frac{A}{H}), \text{angle} = \tan^{-1}(\frac{O}{A}) \).

In a right triangle, the sum of the three angles is always 180 degrees. One angle is always 90 degrees, so the other two angles must add up to 90 degrees.

You can use the Pythagorean theorem: $$c^2 = a^2 + b^2$$ . Here, let c = 21.4 cm and a = 18.0 cm. Solve for b: $$b = \sqrt{c^2 - a^2} = \sqrt{21.4^2 - 18.0^2}$$ .

The area of a right triangle can be calculated using the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ .

To round an angle to the nearest tenth, look at the hundredths place. If it is 5 or greater, round up the tenths place by one. If it is less than 5, keep the tenths place the same.