Answer:
See below
Step-by-step explanation:
Here we need to prove that ,

Imagine a right angled triangle with one of its acute angle as
.
- The side opposite to this angle will be perpendicular .
- Also we know that ,


And by Pythagoras theorem ,

Where the symbols have their usual meaning.
Now , taking LHS ,

- Substituting the respective values,





Since LHS = RHS ,
Hence Proved !
I hope this helps.
Answer:
1) B = 66.5° c = 10.9
Step-by-step explanation:
I will do question one as an example. In general, for these questions you want to use the appropriate trigonometric ratios to solve for the variables and/or apply logic using rules regarding triangles. See attached image for all solving steps.
For side c, we can use Cosine of angle A for a ratio between 10 and c. When we write out the equation, we can solve for side c. So when we write it out, we get the equation:
cos23.5 = ¹⁰⁄c
c = ¹⁰⁄cos₂₃.₅
c = 10.9044 (make sure to round to the nearest tenth, which is one decimal place)
For angle B, since they have given two angles, you can solve for B since all angles of a triangle add up to 180 degrees.
So b = 180 - (90 + 23.5) = 180 - 113.5
b = 66.5
- It is also possible to solve this using sine of angle B and solve it from there, but applying the theory this way is much simpler. (this is on the image if you're curious about it)
I hope this helps you with the other 3 questions.
The radius of cone is 2 inches
<em><u>Solution:</u></em>
<em><u>The volume of cone is given by formula:</u></em>

Where,
"V" is the volume of cone
"r" and "h" are the radius and height of cone respectively
Given that, volume of a cone is 16 pi cubic inches
Its height is 12 inches
Therefore, we get,
V =
cubic inches
h = 12 inches
r = ?
<em><u>Substituting the values in formula, we get</u></em>

Since, radius cannot be negative, ignore r = -2
Thus radius of cone is 2 inches
(x,y,z)=(-4,-2,-5)
I added some images for explanation
<h2>
Question:</h2>
At Priscilla's school, the final grade for her Calculus course is weighted as follows: Tests: 50% Quizzes: 30% Homework: 20% Priscilla has an average of 87% on her tests, 100% on her quizzes, and 20% on her homework. What is Priscilla's weighted average?
<h2>
Work:</h2>
Weighted Average gives weights to each percent of the average as follows:
Weighted Average = Average * weighting percent
Weighted Average = Test Average * Test Weighting + Quiz Average. * Quiz Weighting + Homework Average * Homework Weighting
Weighted Average = 87% * 50% + 100% * 30% + 20% * 20%
Weighted Average = 43.5% + 30% + 4%
Weighted Average = 77.5%
<h2>
Answer:</h2>
77.5%
Learn more:
brainly.com/question/26499519
Graphing
brainly.com/question/26479805
Converting fractions into decimals
Thank You!
Answered by: ms115