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2 years ago

4.

Mathematics

1 answer:

Romashka-Z-Leto [24]2 years ago

5 0

B and d i think i just did it in my head!

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Helpppp pleaseeeeeeeeeeeeeee

Vesna [10]

Answer:

Find below the calculations of the two areas, each with two methods. The results are:

Upper triangle:

$Area=5000\sqrt{3}units^2$

Lower triangle:

$Area=14,530m^2$

Explanation:

A) Method 1

When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:

$Area=side_1\times side_2\times sin(\alpha)$

Where, $\alpha$ is the measure of the included angle.

1. Upper triangle:

$side_1=200units\\ \\ side_2=100units\\ \\ \alpha =60\º\\ \\ Area=200units\times 100units\times sin(60\º)/2\\ \\ Area=5000\sqrt{3}units^2$

2. Lower triangle:

$side_1=231m\\ \\ side_2=150m\\ \\ \alpha =123\º\\ \\ Area=231m\times 150m\times sin(123\º)/2\\ \\ Area=14,529.96m^2\approx14,530m^2$

B) Method 2

You can find the height of the triangle using trigonometric properties, and then use the very well known formula:

$Area=(1/2)\times base\times height$

Use it for both triangles.

3. Upper triangle:

The trigonometric ratio that you can use is:

$sine(\alpha)=opposite\text{ }leg/hypotenuse$

Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:

$sin(60\º)=height/100units\\ \\ height=sin(60\º)\times100units\\ \\ height=50\sqrt{3}units$

$Area=(1/2)\times base\times height=(1/2)\times 200units\times 50\sqrt{3}units=5,000\sqrt{3}units^2$

3. Lower triangle:

$sin(180\º-123\º)=height/231m\\ \\ height=sin(57\º)\times 231m\\ \\ height=193.7329m^2$

$Area=(1/2)\times base\times height=(1/2)\times 150m\times 193.7329m^2\\\\ Area=14,529.96m^2\approx 14,530m^2$

5 0

2 years ago

Simplify 8(7x – 1) + 4(x + 5).

Elina [12.6K]

8(7x-1)+4(x+5)

multiply; 8 x 7=

56x + -1 + 4x +5

reorder the terms;

-1 + 5 + 56x + 4x

Combine like terms; -1 + 5 = 4

4 + 56x + 4x

Combine like terms again; 56x + 4x = 60x

4 + 60x

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2 years ago

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s344n2d4d5 [400]

Answer:

Step-by-step explanation:

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3 years ago

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Sliva [168]

Answer:

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Step-by-step explanation:

I don't see the answer choices that you have, so this is the best I could do! Hoped it helped!

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