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Nana76 [90]
3 years ago
11

If a right triangle has one 30 degree angle and the shortest side is 6, what is the hypotenuse

Mathematics
1 answer:
bulgar [2K]3 years ago
7 0

Answer:

The 30-60-90 degree triangle is in the shape of half an equilateral triangle, cut straight down the middle along its altitude. It has angles of 30°, 60°, and 90°. In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg, you can find the long leg by multiplying the short leg by the square root of 3.

Note: The hypotenuse is the longest side in a right triangle, which is different from the long leg. The long leg is the leg opposite the 60-degree angle.

Two of the most common right triangles are 30-60-90 and the 45-45-90 degree triangles. All 30-60-90 triangles, have sides with the same basic ratio. If you look at the 30–60–90-degree triangle in radians, it translates to the following:

30, 60, and 90 degrees expressed in radians.

A 30-60-90-degree right triangle.

If you know one side of a 30-60-90 triangle, you can find the other two by using shortcuts. Here are the three situations you come across when doing these calculations:

Type 1: You know the short leg (the side across from the 30-degree angle). Double its length to find the hypotenuse. You can multiply the short side by the square root of 3 to find the long leg.

Type 2: You know the hypotenuse. Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg.

Type 3: You know the long leg (the side across from the 60-degree angle). Divide this side by the square root of 3 to find the short side. Double that figure to find the hypotenuse.

Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.

In the triangle TRI in this figure, the hypotenuse is 14 inches long; how long are the other sides?

Because you have the hypotenuse TR = 14, you can divide by 2 to get the short side: RI = 7. Now you multiply this length by the square root of 3 to get the long side:

The long side of a 30-60-90-degree triangle.

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3 years ago
You earn $250 per month from your part-time job. You are in a kayaking club that costs $20 per month, and you save at least $100
Olegator [25]

Answer:

Amounts in the intervall 130 \leq c \leq 230

Step-by-step explanation:

We will take the variables c and s, where

c = amount to spend that month

s = savings of the month.

Since each month we save at least 100, we know that

0 \leq s \leq 100

Moreover, we earn $250 per month and we spend $20 in a kayaking club, which tells us that

250=20+s+c

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230-s=c

By multiplying by -1, the first inequality also tells us that

-100 \leq -s \leq 0

Consequently by adding 230 to the inequality, we get that

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5 0
3 years ago
It costs $5 to get into the fair and then costs $3 for every ride I go on.
Neko [114]

Answer:

26 = 5 + (r×3)

26 - 5 = 21

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3 years ago
A circular flower bed is 19 m in diameter and has a circular sidewalk around it that is 4 m wide. Find the area of the sidewalk
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Answer:

289 m²

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First find the area of the flower bed

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Then get the area of everything including the sidewalk

A=πr²= (3.14)(13.5)² = 572.265

Then subtract and you'll get the area of just the sidewalk

572.265 - 283.385 = 288.88m²

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