GIZMO - Student Exploration - Sine, Cosine, and Tangent Ratios [ANSWER KEY] Updated Latest 2023.

GIZMO - Student Exploration - Sine, Cosine, and Tangent Ratios [ANSWER KEY] Updated Latest 2023. Student Exploration: Sine, Cosine, and Tangent Ratios Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. Vocabulary: angle of elevation, cosine, hypotenuse, leg, right triangle, sine, tangent, trigonometric ratio Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Joseph’s math teacher challenges him to estimate the height of a pine tree next to the school. Joseph walks 9.9 meters from the base of the trunk, lies on his belly, and measures a 45° angle of elevation to the top of the tree. 1. Do you think Joseph has enough information to estimate of the height of the tree? yes Explain. he can use tan to find the height 2. What is your estimate of the height of the tree? 9.9 meters Gizmo Warm-up There are several ways Joseph could estimate the height of the tree. He could draw a right triangle (triangle with a 90° angle) with a side of 9.9 cm and an angle of 45°. Another way to solve the problem is to use trigonometric ratios. These ratios are the subject of the Sine, Cosine, and Tangent Ratios Gizmo. You can use ΔABC to model how Joseph could measure the tree. To begin, check that m∠A is set to 45°. (To quickly set a slider to a value, type the value in the box to the right of the slider and press Enter.) 1. The legs of a right triangle are the two sides that form the right angle, and . The hypotenuse is the side opposite the right angle, . A. Which side of the triangle represents the height of the tree? line BC B. Which side represents the distance from Joseph to the base of the tree? line AC C. Which side represents the distance from Joseph to the top of the tree? line AB 2. Turn on Show side lengths. Based on the lengths, what is the height of the tree? 9.9 meters.