Triangle PRQ is half of an equilateral triangle. If angle P is 30° is What is the value of sec 60° ?
Question
Triangle PRQ is half of an equilateral triangle.
If angle P is 30°
What is the value of sec 60°?
Solution
The secant of an angle in a right triangle is defined as the ratio of the hypotenuse to the adjacent side.
In this case, we are asked to find the secant of 60°.
Step 1: Draw a right triangle with one angle of 60°.
Step 2: Recall the properties of a 30-60-90 triangle. The sides are in the ratio of 1:√3:2.
Step 3: The secant of an angle is the reciprocal of the cosine of the angle.
Step 4: The cosine of 60° is adjacent/hypotenuse = 1/2.
Step 5: Therefore, the secant of 60° is the reciprocal of the cosine of 60°, which is 2/1 = 2.
So, the value of sec 60° is 2.
Similar Questions
The hypotenuse of a 30°-60°-90° triangle is 30. What is the length of one of its legs?
A triangle has one angle of 120 degrees and two equal angles. What is the measure of each of the equal angles?30 degrees90 degrees45 degrees60 degrees
In a right triangle, if one acute angle measures 30 degrees, what is the measure of the other acute angle?Choices:- 30 degrees 45 degrees 60 degrees 90 degrees
n the given figure PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°. Find ∠PCA.
A triangle has angle measurements of 90°, 31°, and 59°. What kind of triangle is it?acuterightobtuseSubmit
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.