📏 trigonometry

1. **State the problem:** Isabella has let out 89 feet of string for her kite, which makes an angle of elevation of 40° with the ground. We need to find the height of the kite abov

1. **State the problem:** A lighthouse is 25 meters above sea level. The angle of depression to a sailboat at sea level is 10°. We need to find the horizontal distance from the bas

1. **State the problem:** We need to find the height of a tree that casts a shadow 21 meters long, given the angle of depression of the sun to the tree is 51°. 2. **Identify the ri

1. **State the problem:** A fireman leans a 36-foot ladder against a building, placing the base 7 feet from the building. We need to find the angle $\theta$ between the ladder and

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