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The Pythagorean theorem is an equation that is used to find the length of a missing side of a right triangle. *If you know the length of two sides of a right triangle, you can use the theorem to solve for the third side.
Cosine is a trig ratio that is used to solve for
the missing side lengths when you are only given the hypotenuse and the adjacent leg in a right triangle.
2
+ (leg)
(leg)
= (hyp)
2
* or a + b = c
Before you learn the concepts of "SohCahToa" and the Pythagorean Theorem, you need to know the parts of the triangle first.
Tangent is a trig ratio that is used to solve
for missing side lengths when you are only given the opposite leg and adjacent leg in a right triangle.
The other 2 legs are the opposite and adjacent legs. The opposite leg is the leg that is across from the reference angle. The adjacent leg is the leg that is next to the reference angle.
Now that you've learned the important parts of the triangle, you will now learn the concepts/trig tools "SohCahToa" and the Pythagorean Theorem.
After being introduced to the main parts of the triangle and to the different trig tools, we will now be solving real world problems using what we learned.
Sine is a trig ratio that is used to solve for the missing side lengths when you are only given the hypotenuse and the opposite leg in a right triangle.
.
opp
hyp
2
:P
250 + 225.1 = h
2
The leg across from the right angle is the hypotenuse.
62500 + 50670.01 = h
113,170.01 = h
A theta is the symbol that represents the unknown degree of an angle in a shape like a right triangle.
2
250 ft.
h= 336.41 ft.
250 ft.
The afternoon sun shined upon a 250ft. skyscraper. The sunlight was blocked by the skyscraper, causing a shadow to form. The distance from the edge of the skyscraper to the tip of it's shadow creates a 48 angle. Find the length of the skyscraper's shadow and then solve for the distance from the edge of the skyscraper to the tip of it's shadow.
o
Y
x
48
o
By Charlene Biacan
Y= 336.41 ft.
Errors: - Forget to square root the sum of the legs.
- Misplacing the legs in the equation.
Tips: - Remember that h means that you have to square it.
- The hypotenuse will have the highest measurement. The rest is legs.
2
225.1 ft.
48
o
2
To solve for "Y," I used the Pythagorean Theorem equation: (leg) +(leg) = (hyp) because I already have two side measurements that I can use to solve for the third side.
There is also "inverse trigonometric ratios," which is used to find the missing angle measurements in a right triangle.
- Using the incorrect trig ratio to
find a missing side/angle.
- Remember "SohCahToa"
if you happen to forget which
trig ratio to use when solving
a problem.
2
- Not labeling the sides of
the right triangle to prevent miscalculations.
- Always label the hypotenuse because
the hypotenuse will always be the longest
side. Always label the triangle.
- Not dividing the equation when the
parentheses is being multiplied by a variable.
- Only divide the equation when the
parentheses is being multiplied by a variable.
2
-1
sin
cos
tan
-1
I solved for "x" first because I had to find the length of the skyscraper's shadow.
tan48
1
=
250
=
(tan48)
x
X(tan48)
(tan48)
250 ft.
X= 225.1 ft.
Errors: -Solving for the hypotenuse first
-Not labeling sides
Tips: - Solve for the topic that the question is asking you to solve first
- Label the sides to prevent confusion
Y
I used tangent to find the shadow's length because I was solving for the adjacent leg and the other leg that had a measurement on it was the opposite leg (250 ft.).
o
X= 225.1 ft.
Since "x" is adjacent to the reference angle (48 ) and the only other side with an actual measurement was the 250 ft. skyscraper (opp. to the reference angle), I decided to use tangent.
48
o