Solve the right triangle.
-$$\mathrm { a } = 2.6 \mathrm {~cm} , \mathrm {~b} = 1.3 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }$$
Round values to one decimal place.
A) $\mathrm { A } = 63.4 ^ { \circ } , \mathrm { B } = 26.6 ^ { \circ } , \mathrm { c } = 2.9 \mathrm {~cm}$
B) $\mathrm { A } = 30.0 ^ { \circ } , \mathrm { B } = 60.0 ^ { \circ } , \mathrm { c } = 3.9 \mathrm {~cm}$
C) $\mathrm { A } = 26.6 ^ { \circ } , \mathrm { B } = 63.4 ^ { \circ } , \mathrm { C } = 2.9 \mathrm {~cm}$
D) $\mathrm { A } = 58.9 ^ { \circ } , \mathrm { B } = 31.1 ^ { \circ } , \mathrm { C } = 2.9 \mathrm {~cm}$

Question

Quizplus · Accepted Answer

To solve the right triangle, we can use trigonometric ratios. Since $\mathrm{C} = 90^\circ$, we can find angle $\mathrm{A}$ using $\tan(A) = \frac{\mathrm{opposite}}{\mathrm{adjacent}} = \frac{1.3}{2.6}$, which gives $\mathrm{A} = 26.6^\circ$. Therefore, $\mathrm{B} = 90^\circ - \mathrm{A} = 63.4^\circ$. To find side $c$, we use the Pythagorean theorem: $c = \sqrt{a^2 + b^2} = \sqrt{2.6^2 + 1.3^2} = 2.9\mathrm{~cm}$.

Solve the Right Triangle a=2.6 cm, b=1.3 cm,C=90∘\mathrm { a } = 2.6 \mathrm {~cm} , \mathrm {~b} = 1.3 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }a=2.6 cm, b=1.3 cm,C=90∘

Solve the Right Triangle $\mathrm { a } = 2.6 \mathrm {~cm} , \mathrm {~b} = 1.3 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }$