Question

Question 2 now you will use geogebra to explore the trigonometric ratios as the acute angle changes in a right triangle. return to trigonometric ratios. move point d until the show side ratios box appears, check the box, and complete each step below. part a move point f to various positions so the measure of ∠a is approximately 15°, 30°, 45°, 60°, and 75°, and record the ratios of the sides of δabc and δade.

Answer 1

To explore the trigonometric ratios as the acute angle changes in a right triangle, use GeoGebra's 'Trigonometric Ratios' tool. Move point D until the 'Show Side Ratios' box appears and check the box. Then, move point F to different positions to change the measure of angle A and record the ratios of the sides of triangles ABC and ADE.

Step-by-step explanation:

Trigonometry is the study of the relationships between the angles and sides of right-angled triangles. In this question, you are asked to use GeoGebra to explore the trigonometric ratios as the acute angle changes in a right triangle.

1. Open GeoGebra and go to the 'Trigonometric Ratios' tool.
2. Move point D until the 'Show Side Ratios' box appears, then check the box.
3. Move point F to various positions so that the measure of angle A is approximately 15°, 30°, 45°, 60°, and 75°.
4. Record the ratios of the sides of triangles ABC and ADE for each angle.

Answer 2

As point F is moved to different positions to create various acute angles for ∠A (approximately 15°, 30°, 45°, 60°, and 75°), the ratios of the sides of triangles ΔABC and ΔADE change accordingly.

Step-by-step explanation:

Exploring the trigonometric ratios in a right triangle using Geogebra involves manipulating point F to alter the acute angle ∠A within approximate measures of 15°, 30°, 45°, 60°, and 75°. With these angle variations, the sides of triangles ΔABC and ΔADE undergo shifts in their ratios.

As point F is adjusted, the values of sine, cosine, and tangent ratios in triangles ΔABC and ΔADE change correspondingly. At 15°, the ratios begin to manifest different proportions in both triangles, illustrating the impact of altering the angle on the side ratios.

Moving point F to approximate 30° showcases another set of ratios, further emphasizing the dynamic relationship between the acute angle and the side lengths in the triangles. This process continues as the angle approaches 45°, 60°, and 75°, showcasing distinct alterations in the trigonometric ratios within both triangles.

Throughout this exploration, the interplay between the acute angle and the side ratios in triangles ΔABC and ΔADE becomes evident, elucidating the fundamental connection between the angle measures and the corresponding trigonometric functions. This exercise underscores the fundamental principles of trigonometry and how changes in acute angles impact the ratios of sides in a right triangle.