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2 years ago

The length of the base of a triangle is twice it’s height. If the area of the triangle is 441 square kilometers, find the height

Mathematics

1 answer:

Sonja [21]2 years ago

5 0

Answer:

21 kilometers

Step-by-step explanation:

Let the height be $x$ . Then, the length of the base is $2x$ . The formula for the area is of the triangle is given by base*height/2. Therefore, the area of the triangle is equal to $\frac{x \cdot 2x}{2} = x^2$ , which is in turn equal to 441. Since $x$ must be positive, then $21^2=441$ , meaning that the height is $21$ kilometers.

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2 years ago

Tickets to a local circus cost $5 for students and $8 for adults. A group of 9 people spent a total of $60. How many adults were

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Answer:

Step-by-step explanation:

You need to set up and solve a system of linear equations here.

Let s and a represent the number of students and adults respectively.

Then s + a = 9, and s = 9 - a.

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3 years ago

A. Name the smallest angle and the largest angle of the following triangles: F 6 S 5 1. A J 5.03 7 5 G B H 5.1 2. D 4 3 E

I am Lyosha [343]

Answer:

(smallest, largest) = (B, C), (D, E), (G, J)

Step-by-step explanation:

Side lengths of a triangle are proportional to the sine of the opposite angle. In a triangle, a larger angle will always have a larger sine. That means the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.

The shortest side is 5 units, opposite angle B. The longest side is 7 units, opposite angle C.

smallest angle: B
largest angle: C

The shortest side is 3 units, opposite angle D. The longest side is 5 units, opposite angle E.

smallest angle: D
largest angle: E

The shortest side is 5 units, opposite angle G. The longest side is 5.1 units, opposite angle J.

smallest angle: G
largest angle: J

_____

<em>Additional comment</em>

Angles in a triangle may exceed 90°. The sine function actually is decreasing for angles above 90°. However, since the total of angles of a triangle must be exactly 180°, there <em>cannot be two angles in a triangle such that the smaller angle has the larger sine</em>.

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