Question

Please answer this math question asap!! 22 points and brainliest!!
BRAINLIEST ONLY IF YOU SHOW YOUR WORK!
MUST SHOW WORK!

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{\angle D\approx22.3\degree}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Length \: of \:EF= 8 \\ \\ \tt: \implies Length \: of \: DF= 21\\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies \angle D= ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Sin \: \theta = \frac{Perpendicular}{Hypotenuse} \\ \\ \tt: \implies Sin \: D = \frac{ef}{df} \\ \\ \tt: \implies Sin \: D = \frac{8}{21} \\ \\ \tt: \implies Sin \: D= 0.38 \\ \\ \tt: \implies Sin \: D = Sin \: 22.33 \\ \\ \green{\tt: \implies \angle D \approx 22.3 \degree}\\ \\ \purple{\bold{Some \: extra \: information}} \\ \pink{\tt{\circ \: Sin \: \theta = \frac{p}{h} }} \\ \\ \pink{\tt{\circ \: Cos \: \theta = \frac{b}{h} }} \\ \\ \pink{\tt{\circ \: Cot \: \theta = \frac{b}{p} }} \\ \\ \pink{\tt{\circ \: Cosec \: \theta = \frac{h}{p} }} \\ \\ \pink{\tt{\circ \: Sec \: \theta = \frac{h}{b} }} \\ \\ \pink{\tt\circ \: {Sin}^{2} \theta + Cos^{2} = 1}$

Answer 2

$</p><p>\huge {\tt{\purple{Hello!!! }}}$

$</p><p>\huge {\fbox{\fbox{\rightarrow {\mathfrak {\pink{Question \: - }}}}}}$

Determine the measure of angle D to the nearest tenth if a degree.

$</p><p>\huge {\fbox{\fbox{\rightarrow {\mathfrak {\red{Solution \: - }}}}}}$

$</p><p>\tt{\purple{Angle \: D \: = \: 22.3 ° }}$

$</p><p>\tt{\underline {\underline {\orange {Step-By-Step-Explaination \:: }}}}$

$</p><p>\tt{\blue{Given = > }}$

$\tt{\purple{DF \: = \: 10 \: cm . }}$

$\tt{\red{EF\: = \: 8 cm . }}$

We Know That :

$</p><p>\tt{\boxed{\boxed{\green{ Sin \: ( \theta ) \: = \frac{Perpendicular}{Hypotenuse} }}}}$

$</p><p>\tt{\boxed{\boxed{\purple{卐 Sin \: ( \theta ) \: = \frac{P}{H} = \frac{DF}{EF} = \frac{8}{21} = 0.38 \: = \: Sin (22.3°)}}}}$

$</p><p>\tt{\purple{\therefore{Angle \: D \: = \: 22.3 ° }}}$

$</p><p>\huge{\fbox{\fbox{\rightarrow{\mathfrak{\green{Additional \: Information \: - }}}}}}$

Identities :

$</p><p>\tt{\boxed{\boxed{\red{卐 Sin \: ( \theta ) \: = \frac{P}{H} }}}}$

$</p><p>\tt{\boxed{\boxed{\orange{卐 Cos \: ( \theta ) \: = \frac{B}{H} }}}}$

$</p><p>\tt{\boxed{\boxed{\purple{卐 Cosec \: ( \theta ) \: = \frac{H}{P} }}}}$

$</p><p>\tt{\boxed{\boxed{\red{卐 Sec \: ( \theta ) \: = \frac{H}{P} }}}}$

$</p><p>\tt{\boxed{\boxed{\orange{卐 Tan \: ( \theta ) \: = \frac{P}{B} }}}}$

$</p><p>\tt{\boxed{\boxed{\purple{卐 Cot \: ( \theta ) \: = \frac{B}{P} }}}}$