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3 years ago

Solve the triangle for x.

Mathematics

1 answer:

Damm [24]3 years ago

4 0

Answer:

d) 86.2 degrees

x = 86.20°

Attached is the image used in the question;

Step-by-step explanation:

Applying the law of cosine;

Cos C = (a² + b² - c²)/2ab

Where;

Angle C = x

c = 13 ft

b = 9ft

a = 10ft

Substituting into the equation;

Cos x = (10² + 9² - 13²)/(2×10×9)

Cos x = 0.0667

x = cos⁻¹(0.0667)

x = 86.20°

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3 years ago

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Two cargo ships spot a signal fire on a small island. The captains know they are 140 feet

Irina18 [472]

The distance from Ship B to the signal fire at point C is $405.4 \mathrm{ft}$

Explanation:

It is given that two ships A and B are at a distance 140 ft from each other.

The angle formed by ship A is 82º and the angle formed by ship B is 78º.

To determine the distance from ship B to the signal fire at point C, we need to know the another angle.

Hence, we have,

$\begin{aligned}\angle A+\angle B+\angle C &=180^{\circ} \\82^{\circ}+78^{\circ}+\angle C &=180^{\circ} \\160^{\circ}+\angle C &=180^{\circ} \\\angle C &=20^{\circ}\end{aligned}$

Now, we shall solve the problem using the law of sines,

$\frac{\sin A}{a}=\frac{\sin C}{c}$

Substituting the values, we have,

$\frac{\sin 82^{\circ}}{a}=\frac{\sin 20^{\circ}}{140}$

$\frac{0.9903}{a}=\frac{0.3420}{140}$

Simplifying, we get,

$a=\frac{0.9903 \times 140}{0.3420}$

$a=405.4$

Thus, the distance from Ship B to the signal fire at point C is $405.4 \mathrm{ft}$

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3 years ago

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3 years ago

Denise has a business where she prints and sells business cards. Each box sold contains 250 business cards. If Denise sold 93 bo

mote1985 [20]

Answer:

23,250

Step-by-step explanation:

250 multiplied by 93 will equal to 23,250

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3 years ago

What is the length of a rectangle with an area of 8/10 square feet and a width of 2 1/4

crimeas [40]

Answer:

The length of the rectangle=16/45 feet

Step-by-step explanation:

The area of a rectangle is given by;

A=L×W

where;

A=area of the rectangle

L=length of the rectangle

W=width of the rectangle

In our case;

A=(8/10) square feet

L=unknown

W=2 1/4 feet=9/4 feet

replacing;

8/10=l×9/4

l=8/10×4/9

l=16/45 feet

The length of the rectangle=16/45 feet

3 0

3 years ago