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3 years ago

A regular triangular pyramid has slant height 6 cm and base edges of length 15 cm. Find: Volume and surface area of the pyramid

Mathematics

1 answer:

just olya [345]3 years ago

7 0

Step-by-step explanation:

the number of members in A municipal corporation depends upon the _______ city

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Find the longer leg of the triangle.

Paha777 [63]

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

The length of the hypotenuse (the side opposite to the right angle) is given.
The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let $\text{Opposite}$ denotes the length of the side opposite to the $30^{\circ}$ acute angle, and $\text{Adjacent}$ be the length of the side next to this $30^{\circ}$ acute angle.

$\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}$ .

Similarly,

$\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}$ .

The longer leg in this case is the one adjacent to the $30^{\circ}$ acute angle. The answer will be $3$ .

There's a shortcut to the answer. Notice that $\sin{30^{\circ}} < \cos{30^{\circ}}$ . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the $30^{\circ}$ angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship $\sin{\theta} < \cos{\theta}$ holds for all acute angles? (That is, $0^{\circ} < \theta$ ?) It turns out that:

$\sin{\theta} < \cos{\theta}$ if $0^{\circ} < \theta$ ;
$\sin{\theta} > \cos{\theta}$ if $45^{\circ} < \theta$ ;
$\sin{\theta} = \cos{\theta}$ if $\theta = 45^{\circ}$ .

4 0

3 years ago

Read 2 more answers

One focus of a hyperbola is located at (-7, 1). One vertex of the hyperbola is located at

inna [77]

Answer:

(x+2)^2/16 - (y-1)^2/9 = 1

Step-by-step explanation:

I just did this problem for edgen 2020.

8 0

2 years ago

Read 2 more answers

Can someone tell me if i did this right lol

baherus [9]

Answer:

Your calculation is correct, but I'd answer 33.0 in.

Step-by-step explanation:

You are correct. Good job.

6 0

2 years ago

Read 2 more answers

Help ...........................................................................

Lynna [10]

Answer: D

Step-by-step explanation: $\frac{2}{6} =\frac{1}{3} = 0,(3)$

7 0

3 years ago

Kendra hiked each day for a week the first day she hiked 1/8 mile the second day she hiked 3/8 mile and the third day she hiked

tigry1 [53]

The question requires us to find out by how much did Kendra increased her distance every day:
The first day she hiked 1/8 miles
the second day she hiked 3/8 miles
third day she hiked 5/8 miles
this can be written as arithmetic sequence given by:
1/8,3/8,5/8,...
the arithmetic difference will be:
3/8-1/8=5/8-3/8=2/8
This means that Kendra increased her daily distance by 2/8 miles

7 0

3 years ago