📏 trigonometry

1. **State the problem:** Sean leaned a 12-foot ladder against his house forming a 68° angle with the ground. We need to find the distance from the base of the house to the base of

1. **State the problem:** We have a right triangle with one leg measuring 11 units adjacent to a 70° angle, and we want to find the length of the side opposite the 70° angle, label

1. The problem asks to find the value of the trigonometric ratio \( \tan A \) given the sides 20 and 21. 2. Recall the definition of tangent in a right triangle: \( \tan(\theta) =

1. The problem asks how to determine the function values (sine or cosine) for given angles and how to identify if these values are positive, negative, or zero based on points on th

1. **Problem:** Convert 200° into radians. 2. **Formula:** To convert degrees to radians, use the formula:

1. **Problem 10:** Given bearings: B from A is 070°, C from A is 120°, and C from B is 125°. (a) Find the bearing of A from C.

1. **State the problem:** We have a right triangle with a right angle at vertex P. The side opposite the 23° angle (at vertex O) is 43 units, and we want to find the length of side

1. **State the problem:** Convert the polar coordinates $\left(6\sqrt{2}, \frac{3\pi}{2}\right)$ into rectangular coordinates $(x,y)$. 2. **Recall the formulas:** For polar coordin

1. Problem: In the right triangle with right angle at C, the hypotenuse AB = 12 cm and angle A = $25^\circ$, and side BC is $a$, find $a$.\n2. Formula and rules: For right triangle

1. Statement of the problem. Find the length of side $a$ in a right triangle where angle $A=30^\circ$ and the hypotenuse is 10.

1. **State the problem:** We have a right triangle with angle $A = 32.4^\circ$, side $b = 48$ opposite angle $B$, and right angle $C = 90^\circ$. We need to find angle $B$, side $a

1. **State the problem:** Solve the right triangle with given angle $A=32.5^\circ$, side $b=34$, and angle $B=57.5^\circ$. Find side $a$, side $c$, and verify angles. 2. **Recall t

1. The problem is to understand the trigonometric relationship involving sine of an angle $\theta$ in a right triangle. 2. The sine of an angle $\theta$ is defined as the ratio of

1. The problem asks to find the length of the hypotenuse $h$ in two right-angled triangles given an angle and one side length. 2. We use the trigonometric functions sine, cosine, o

1. **Stating the problem:** We have a triangle HPT with sides TP = 90 m, TH = 245 m, and angle \(\angle HTP = 13^\circ\). We want to verify the given answers:

1. **State the problem:** Find equivalent ratios in terms of the acute angle and then find the exact value of $\tan 150^\circ - \sin 135^\circ$.\n\n2. **Recall angle relationships:

1. **State the problem:** Find equivalent ratios in terms of acute angles and then find the exact value of the expression $\tan 150^\circ - \sin 135^\circ$.\n\n2. **Recall angle re

1. **State the problem:** Calculate $\tan 150^\circ - \sin 135^\circ$.\n\n2. **Recall the formulas and values:**\n- $\tan(180^\circ - \theta) = -\tan \theta$.\n- $\sin(180^\circ -

1. **State the problem:** We are given a right triangle with vertices A, B, and C, where angle C is the right angle.

1. **Problem statement:** We have two right triangles. For the first triangle ABC with right angle at C, sides BC=8, AC=6, and hypotenuse AB=10, find the six trigonometric ratios f

1. **State the problem:** We have a truck on a ramp that forms a right triangle. The ramp length (hypotenuse) is 75 feet, and the vertical height is $x$. We want to find the tippin