question 19 of 25

in $\delta jkl$, $m\angle j = 90^\circ$, $m\angle k = 30^\circ$, and $m\angle l = 60^\circ$. which of the following statements about $\delta jkl$ are true?

check all that apply.

a. $jk = 2 \cdot jl$
b. $kl = \sqrt{3} \cdot jl$
c. $jk = \sqrt{3} \cdot jl$
d. $jl = \frac{\sqrt{3}}{2} \cdot kl$
e. $jk = \frac{\sqrt{3}}{2} \cdot kl$
f. $kl = 2 \cdot jl$

Question

question 19 of 25

in $\delta jkl$, $m\angle j = 90^\circ$, $m\angle k = 30^\circ$, and $m\angle l = 60^\circ$. which of the following statements about $\delta jkl$ are true?

check all that apply.

a. $jk = 2 \cdot jl$
b. $kl = \sqrt{3} \cdot jl$
c. $jk = \sqrt{3} \cdot jl$
d. $jl = \frac{\sqrt{3}}{2} \cdot kl$
e. $jk = \frac{\sqrt{3}}{2} \cdot kl$
f. $kl = 2 \cdot jl$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "30-60-90 Triangle Properties" ], "new_concepts": [], "current_concepts": [ "30-60-90 Triangle Properties", "Special Right Triangles" ] } ## Identify the triangle type and side relationships Using the *30-60-90 Triangle Properties* knowledge point $$ \begin{aligned} &\text{In } \Delta JKL, \text{ the angles are } m\angle J = 90^\circ, m\angle K = 30^\circ, m\angle L = 60^\circ.\ &\text{The side opposite } 30^\circ \text{ is } JL \text{ (shorter leg, } x\text{)}.\ &\text{The side opposite } 60^\circ \text{ is } JK \text{ (longer leg, } x\sqrt{3}\text{)}.\ &\text{The side opposite } 90^\circ \text{ is } KL \text{ (hypotenuse, } 2x\text{)}. \end{aligned} $$ ## Express side lengths in terms of JL Using the *30-60-90 Triangle Properties* knowledge point $$ \begin{aligned} &KL = 2 \cdot JL\ &JK = \sqrt{3} \cdot JL \end{aligned} $$ ## Express side lengths in terms of KL Using the *30-60-90 Triangle Properties* knowledge point $$ \begin{aligned} &JL = \frac{1}{2} \cdot KL\ &JK = \frac{\sqrt{3}}{2} \cdot KL \end{aligned} $$ ## Evaluate the given statements Using the *30-60-90 Triangle Properties* knowledge point $$ \begin{aligned} &\text{A. } JK = 2 \cdot JL \quad (\text{False, } JK = \sqrt{3} \cdot JL)\ &\text{B. } KL = \sqrt{3} \cdot JL \quad (\text{False, } KL = 2 \cdot JL)\ &\text{C. } JK = \sqrt{3} \cdot JL \quad (\text{True})\ &\text{D. } JL = \frac{\sqrt{3}}{2} \cdot KL \quad (\text{False, } JL = \frac{1}{2} \cdot KL)\ &\text{E. } JK = \frac{\sqrt{3}}{2} \cdot KL \quad (\text{True})\ &\text{F. } KL = 2 \cdot JL \quad (\text{True}) \end{aligned} $$

A. $JK = 2 \cdot JL$

B. $KL = \sqrt{3} \cdot JL$

C. $JK = \sqrt{3} \cdot JL$

D. $JL = \frac{\sqrt{3}}{2} \cdot KL$

E. $JK = \frac{\sqrt{3}}{2} \cdot KL$

F. $KL = 2 \cdot JL$

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QUESTION IMAGE

Question

Explanation:

Identify the triangle type and side relationships

Express side lengths in terms of JL

Express side lengths in terms of KL

Evaluate the given statements

Answer: