Answer:
7. one triangle
8. two triangles
Step-by-step explanation:
When you are given two sides and one of the opposite angles, you can make a determination as follows:
- If the given angle is <em>opposite the longest given side</em>, there is one solution.
- If the given angle is <em>opposite the shortest given side</em>, there may be 0, 1, or 2 solutions.
For the latter case, the possibilities for sides b, c, and angle C are ...
C > 90° . . . . . . . . no solution
(b/c)sin(C) > 1 . . . no solution
(b/c)sin(C) = 1 . . . 1 solution
(b/c)sin(C) < 1 . . . 2 solutions
(The expression (b/c)sin(C) gives sin(B), so the value must lie within the range of the sine function in order for there to be any solution.)
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7. The given angle is opposite the <em>longest</em> given side. There is one solution.
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8. The given angle is opposite the <em>shortest</em> given side, so we compute
(b/c)sin(C) = (34/28)sin(20°) ≈ 0.41
This is less than 1, so there are two solutions.
Answer:
Step-by-step explanation:
The idea here is to find the value for x and y, then add them together. See the pic I attached below. We will solve for side x first.
Side s is across from the reference angle of 48 degrees; side measuring 50 m is adjacent to the reference angle 48 degrees. Therefore, we will use the tangent ratio to solve for x:
and
50tan(48) = x so
x = 55.53m
Now we will do the same and solve for y. This time the reference angle is 28 degrees. Side y is opposite the reference angle and the side measuring 50 is adjacent to the reference angle, so we will use the tangent ratio again:
and
50tan(28) = y so
y = 26.59. Therefore,
x + y = 55.53 + 26.59 and
the height of the taller building is
82.1 m
Let's simplify step-by-step. <span><span><span>−<span>3<span>(<span><span><span>4x</span>−<span>5y</span></span>+6</span>)</span></span></span>+<span>8x</span></span>−9</span>
<span />Distribute:<span>=<span><span><span><span><span><span><span> (<span>−3</span>)</span><span>(<span>4x</span>)</span></span>+<span><span>(<span>−3</span>)</span><span>(<span>−<span>5y</span></span>)</span></span></span>+<span><span>(<span>−3</span>)</span><span>(6)</span></span></span>+<span>8x</span></span>+</span>−9</span></span><span>=<span><span><span><span><span><span><span> −<span>12x</span></span>+<span>15y</span></span>+</span>−18</span>+<span>8x</span></span>+</span>−9</span></span>
<span><span /></span>Combine Like Terms:<span>= <span><span><span><span><span>−<span>12x</span></span>+<span>15y</span></span>+<span>−18</span></span>+<span>8x</span></span>+<span>−9</span></span></span><span>=<span><span><span> (<span><span>−<span>12x</span></span>+<span>8x</span></span>)</span>+<span>(<span>15y</span>)</span></span>+<span>(<span><span>−18</span>+<span>−9</span></span>)</span></span></span><span>=<span><span><span> −<span>4x</span></span>+<span>15y</span></span>+<span>−27</span></span></span>
<span><span><span /></span></span>Answer <span>=<span><span><span> −<span>4x</span></span>+<span>15y</span></span>−<span>27</span></span></span>
64+(2x)=35(x-1)
expand
64+2x=35x-35
minus 2x from both sides
64=33x-35
add 35 to both sides
99=33x
divide both sides by 33
3=x
the number is 3
3 feet because 3x2( twice it’s width ) is 6 plus 1 ( one foot more ) is 7