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Lesson Topics Discussion Quiz: Class Homework

Example1

Title: Trigonometry

Grade Lesson s5-p2

Explanation: The best way to understand SAT-4 is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1 Example2

In triangle XYZ, angle X measures 48°, angle Y measures 64°, and side XZ measures 16 units. Find the lengths of sides XY and YZ.

Step: 1

To find the lengths of sides XY and YZ in triangle XYZ, we can use the law of sines, which states:
\$"a"/("sin""A") = "b"/("sin""B") = "c"/("sin""C")\$

Given that angle X measures 48° and side XZ measures 16 units, we can find angle Z using the fact that the sum of angles in a triangle is 180°:
Z = 180 - ( X + Y)
Z = 180 - ( 48 + 64)
Z = 68°

Explanation:

Here, introduce the law of sines formula and then find the angle Z value.

Step: 2

Now apply the law of sines to find the lengths of sides XY.

\$("XY")/("sin""X") = ("XZ") / ("sin""Z")\$

\$("XY")/("sin"(48)) = 16/("sin"(68))\$

\$"XY" = (16 times "sin"(48))/("sin"(68))\$
XY = 12.81 units

Explanation:

Here, use the law of sines rule for find the length of XY.

Step: 3

Now apply the law of sines to find the lengths of sides YZ.

\$("YZ") / ("sin""Y") = ("XZ") / ("sin""Z")\$

\$("YZ")/("sin"(64)) = 16/("sin"(68))\$

\$"YZ" = (16 times "sin"(64))/("sin"(68))\$

YZ = 15.5 units

So, the sides XY and YZ lengths are approximately 12.81 units and 15.5 units, respectively.

Explanation:

Here also use the law of sines rule for find the length of YZ.

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