solve this question pls i will mark you brainlist
Answers
Answer:
option 3 is correct
30,60,90
Step-by-step explanation:
the sum of interior angles of triangle is 180
30+60+90 = 180
Answer:
Home > 30°-60°-90° Triangle – Explanation & Examples
30°-60°-90° Triangle – Explanation & Examples
When you’re done with and understand what a right triangle is and other special right triangles, it is time to go through the last special triangle — the 30°-60°-90° triangle.
It also carries equal importance to the 45°-45°-90° triangle due to the relationship of its side. It has two acute angles and one right angle.
What is a 30-60-90 Triangle?
A 30-60-90 triangle is a special right triangle whose angles are 30º, 60º, and 90º. The triangle is special because its side lengths are always in the ratio of 1: √3:2.
Any triangle of the form 30-60-90 can be solved without applying long-step methods such as the Pythagorean Theorem and trigonometric functions.
The easiest way to remember the ratio 1: √3: 2 is to memorize the numbers; “1, 2, 3”. One precaution to using this mnemonic is to remember that 3 is under the square root sign.
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From the illustration above, we can make the following observations about the 30-60-90 triangle:
The shorter leg, which is opposite to the 30- degree angle, is labeled as x.
The hypotenuse, which is opposite to the 90-degree angle, is twice the shorter leg length (2x).
The longer leg, which is opposite to the 60-degree angle, is equal to the shorter leg’s product and the square root of three (x√3).
How to Solve a 30-60-90 Triangle?
Solving problems involving the 30-60-90 triangles, you always know one side, from which you can determine the other sides. For that, you can multiply or divide that side by an appropriate factor.
You can summarize the different scenarios as:
When the shorter side is known, you can find the longer side by multiplying the shorter side by a square root of 3. After that, you can apply Pythagorean Theorem to find the hypotenuse.
When the longer side is known, you can find the shorter side by diving the longer side by the square root of 3. After that, you can apply Pythagorean Theorem to find the hypotenuse.
When the shorter side is known, you can find the hypotenuse by multiplying the shorter side by 2. After that, you can apply Pythagorean Theorem to find the longer side.
When the hypotenuse is known, you can find the shorter side by dividing the hypotenuse by 2. After that, you can apply Pythagorean Theorem to find the longer side.
This means the shorter side acts as a gateway between the other two sides of a right triangle. You can find the longer side when the hypotenuse is given or vice versa, but you always have to find the shorter side first.
Also, to solve the problems involving the 30-60-90 triangles, you need to be aware of the following properties of triangles:
The sum of interior angles in any triangle adds up to 180º. Therefore, if you know the measure of two angles, you can easily determine the third angle by subtracting the two angles from 180 degrees.
The shortest and longest sides in any triangle are always opposite to the smallest and largest angles. This rule also applies to the 30-60-90 triangle.
Triangles with the same angle measures are similar, and their sides will always be in the same