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3 years ago

A line passes through the point (-8, -3) and has a slope of -3/2

Mathematics

1 answer:

rjkz [21]3 years ago

4 0

Answer:

this is the answer

Step-by-step explanation:

hope it helped!!!

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Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).

Therefore, AB must be exactly half of AD:

$AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24$

3 0

3 years ago

Read 2 more answers

Is 0.6 repeating a rational number

julsineya [31]

Any decimal number that is repeating can be written in the form $\frac{a}{b}$ with b not equal to zero, so they are rational numbers.

The short answer is yes, 0.6 repeating is a rational number.

Hope this helped :)

6 0

3 years ago

Evaluate a +6 for a = 10. NEXT QUESTION © ASK FOR HELP

eduard

Answer:

Step-by-step explanation:

10+6=16

5 0

3 years ago

A number k plus 19.5 is less than or equal to 40

Yuri [45]

K+19.5≤ 40
You can then proceed to solve the inequality

3 0

3 years ago

Jordan is a student who hates to be called on in class. His teacher randomly calls on students and Jordan knows that on any give

Anika [276]

Answer:

0.1 for each case

Step-by-step explanation:

Because Jordan's teacher randomly calls on students and Jordan has 10% chance of being called on any given day, the probability that on the first day Jordan is called on is 0.1 Besides, the probability remains constant on any given day, so, the probability that on the 2nd day Jordan is called on is 0.1 and for the 5th day is the same 0.1 Probability is always a number between 0 and 1.

7 0

3 years ago