Verified answer

✏️TRIANGLE

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[tex] \underline{\mathbb{DIRECTIONS:}} [/tex]

• Find the missing sides and angle of the given triangle.

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[tex] \underline{\mathbb{ANSWERS:}} [/tex]

[tex] \qquad\Large\rm» \:\: 1. \: \green{b = 4} [/tex]

[tex] \qquad\Large\rm» \:\: 2. \: \green{c = 8} [/tex]

[tex] \qquad\Large\rm» \:\: 3. \: \green{m\angle B = 45 \degree} [/tex]

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[tex] \underline{\mathbb{SOLUTIONS:}} [/tex]

No. 1:

» Apply the Tangent Ratio.

• [tex] \tan \theta = \frac{ \: opp. \: }{adj.} \\ [/tex]

• [tex] \tan A = \frac{ \: a \: }{b} \\ [/tex]

• [tex] \tan 45 \degree = \frac{ \: 4 \: }{b} \\ [/tex]

• [tex]1 = \frac{ \: 4 \: }{b} \\ [/tex]

• [tex]b= \frac{ \: 4 \: }{1} \\ [/tex]

• [tex]b = 4[/tex]

[tex] \therefore [/tex] The value of b is 4.

[tex] \rm [/tex]

No. 2:

» Apply the Sine Ratio.

• [tex] \sin \theta = \frac{ \: opp. \: }{hyp.} \\ [/tex]

• [tex] \sin A = \frac{ \: a \: }{c} \\ [/tex]

• [tex] \sin 45 \degree = \frac{ \: 4 \: }{c} \\ [/tex]

• [tex] \frac{ \: 1 \: }{2} = \frac{ \: 4 \: }{c} \\ [/tex]

• [tex]c = 8[/tex]

[tex] \therefore [/tex] The value of c is 8.

[tex] \rm [/tex]

No. 3:

» Angle BCA is a right angle measuring 90 degree. Therefore,

• [tex] \rm m\angle A + m\angle B = 90 \degree[/tex]

• [tex] \rm 45 \degree + m\angle B = 90 \degree[/tex]

• [tex] \rm m\angle B = 90 \degree - 45 \degree[/tex]

• [tex] \rm m\angle B = 45\degree[/tex]

[tex] \therefore [/tex] The measure of angle B is 45 degrees.

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