All HiSET: Math Resources
Example Questions
Example Question #1 :问题涉及直角三角形三角
Evaluatein terms of.
Suppose we allowbe the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring.
The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, so
We can set the lengths of the opposite and adjacent legs toand 5, respectively. The length of the hypotenuse can be determined using the Pythagorean Theorem:
The sine of the angle is equal to the ratio of the length opposite leg to that of the hypotenuse, so
.
Example Question #1 :问题涉及直角三角形三角
Evaluatein terms of.
Suppose we allowbe the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring. The cosine is defined to be the ratio of the length of the adjacent side to that of the hypotenuse, so
We can set the lengths of the adjacent leg and the hypotenuse toand 3, respectively. By the Pythagorean Theorem, the length of the opposite leg is
The sine of the angle is equal to the ratio of the length of the opposite leg to that of the hypotenuse, so
.
Example Question #1 :问题涉及直角三角形三角
Evaluatein terms of.
Suppose we allowbe the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring.
The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, so
We can set the lengths of the opposite and adjacent legs toand 5, respectively. The length of the hypotenuse can be determined using the Pythagorean Theorem:
The cosine of the angle is equal to the ratio of the length of the adjacent leg to that of the hypotenuse, so
.
Example Question #1 :问题涉及直角三角形三角
None of the other choices gives the correct response.
None of the other choices gives the correct response.
An identity of trigonometry is
for any value of.
Since, it immediately follows that.
This response is not among the given choices.
Example Question #1 :Tangent
Refer to the triangle in the above diagram. Which of the following expressions correctly gives its area?
None of the other choices gives the correct response.
The area of a right triangle is half the product of the lengths of its legs, which here areand- that is,
We are given that.is the leg opposite the angleandis its adjacent leg, we can findusing the tangent ratio:
Settingand, we get
Solve forby multiplying both sides by 12:
Now, setandin the area formula:
,
the correct choice.
Example Question #1 :Tangent
Refer to the triangle in the above diagram. Which of the following expressions correctly gives its area?
None of the other choices gives the correct response.
The area of a right triangle is half the product of the lengths of its legs, which here areand- that is,
We are given that.is the leg opposite the angleandis its adjacent leg, we can findusing the tangent ratio:
Settingand, we get
Solve forby first, finding the reciprocal of both sides:
Now, multiply both sides by 8:
Now, setandin the area formula:
,
the correct choice.
Example Question #1 :Tangent
Evaluatein terms of.
Suppose we allowbe the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring. The cosine is defined to be the ratio of the length of the adjacent side to that of the hypotenuse, so
We can set the lengths of the adjacent leg and the hypotenuse toand 3, respectively. By the Pythagorean Theorem, the length of the opposite leg is
The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, so
.
Example Question #1 :问题涉及直角三角形三角
The sine of an angle is defined to be the ratio of the length of the opposite leg of a right triangle to the length of its hypotenuse. Therefore, we can set. By the Pythagorean Theorem:
the adjacent leg of the triangle has measure
The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, which is
,
the correct response.
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