Answer:
The ratios of the sides of a right triangle are called trigonometric ratios. We need to use trigonometric functions to find them when we don't have any angle other than 90 degree shown.
Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan). These are defined for acute angle.
However when we have one angle given with the 90 degree we can deduct without trigonometry but we would use all angles to find the hypotenuse or all angles to find the side of a right angle.
Alternatively, we cna do this with one given angle but if we have one, we might as well work out the other one without trigonometry and do a division with Sin = 25 (sin 35) sin 90 / sin 55
is one example when given the base 25ft that would find the hypotenuse or the length of elevation for buildings looking down or zip-wire questions.
Step-by-step explanation:
A
| \
l \
4cm| \ 5cm
| \
| \
B | - - - - \ C
3cm
Suppose we wanted to find sin( A) in△ABC
(The height of the wall in elevation questions would be used above the base shown 3cm at the start) Sin = 3 (sin 35)° sin 90° / sin 55° to find the height side (4).
Sine is defined as the ratio of the opposite to the hypotenuse
sin(A) = hypotenuse = AB/BC = 3/5
/ opposite
D
The domain is the x values, so the right side of the circle are the x’s.
Answer:
12.1 cm
Step-by-step explanation:
Using the law of sines, we can find angle C. Then from the sum of angles, we can find angle B. The law of sines again will tell us the length AC.
sin(C)/c = sin(A)/a
C = arcsin((c/a)sin(A)) = arcsin(8.2/13.5·sin(81°)) ≈ 36.86°
Then angle B is ...
B = 180° -A -C = 180° -81° -36.86° = 62.14°
and side b is ...
b/sin(B) = a/sin(A)
b = a·sin(B)/sin(A) = 13.5·sin(62.14°)/sin(81°) ≈ 12.0835
The length of AC is about 12.1 cm.
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<em>Comment on the solution</em>
The problem can also be solved using the law of cosines. The equation is ...
13.5² = 8.2² +b² -2·8.2·b·cos(81°)
This is a quadratic in b. Its solution can be found using the quadratic formula or by completing the square.
b = 8.2·cos(81°) +√(13.5² -8.2² +(8.2·cos(81°))²)
b = 8.2·cos(81°) +√(13.5² -(8.2·sin(81°))²) . . . . . simplified a bit
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Answer: the slope is 2
Step-by-step explanation:
It goes up 2 and over 1
y/x
rise over run= rise/run
