In triangle ABC, with right angle at B, angle A is congruent to angle C. Find the value of (sin A cos C) + (cos A sin C).
Question
In triangle ABC, with right angle at B, angle A is congruent to angle C. Find the value of (sin A cos C) + (cos A sin C).
Solution
In a right triangle, the sum of the two non-right angles is 90 degrees. Given that angle A is congruent to angle C, this means that each of these angles is 45 degrees.
The sine and cosine of a 45-degree angle are both equal to √2/2.
Therefore, sin A = cos C = √2/2 and cos A = sin C = √2/2.
Substituting these values into the expression (sin A cos C) + (cos A sin C), we get:
(√2/2 * √2/2) + (√2/2 * √2/2) = 1/2 + 1/2 = 1.
So, the value of (sin A cos C) + (cos A sin C) is 1.
Similar Questions
Triangle ABC is congruent to triangle DEF.
In triangle ABC, angle B is right angled, AC=2 and
(ii) Convert the products of sine A and cos C into the sum form of trigonometric functions of the triangle above.
cos(90–A) and sinA are
Solve the triangle shown in the following figure using the Law of Sines. (Enter all angles in degrees. Round your answers to one decimal place.)6.13.170°A triangle is given.The angle at vertex A is 70°.The side opposite vertex A has length 6.1.The side opposite vertex B has length 3.1.c = ∠B = °∠C = °
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.