20. in △lmn, if |lm| = 6 cm, ∠lmn = 90°, ∠lnm = x and sin x = 3/5. find the area of △lmn. a. 60 cm² b. 48…

20. in △lmn, if |lm| = 6 cm, ∠lmn = 90°, ∠lnm = x and sin x = 3/5. find the area of △lmn. a. 60 cm² b. 48 cm² c. 24 cm² d. 30 cm² 21. consider the statements: p: all students offering literature(l) also offer history(h); q: students offering history(h) do not offer geography(g). which of the venn diagrams correctly illustrate the two statements? a. venn - diagram image description b. venn - diagram image description c. venn - diagram image description d. venn - diagram image description

Answer

Question 20

Explanation:

Step1: Find cosine value

Since $\sin x=\frac{3}{5}$ and $\angle LMN = 90^{\circ}$, using $\sin^{2}x+\cos^{2}x = 1$, we have $\cos x=\sqrt{1 - \sin^{2}x}=\sqrt{1-(\frac{3}{5})^{2}}=\sqrt{1-\frac{9}{25}}=\sqrt{\frac{16}{25}}=\frac{4}{5}$.

Step2: Find side - lengths

Let $LN$ be the hypotenuse. If we assume the opposite side to $\angle LNM$ (side $LM$) is $a = 6$ cm and $\sin x=\frac{LM}{LN}=\frac{3}{5}$, then $LN=\frac{LM}{\sin x}=\frac{6}{\frac{3}{5}} = 10$ cm. Using the Pythagorean theorem or $\cos x=\frac{MN}{LN}$, we get $MN = LN\times\cos x=10\times\frac{4}{5}=8$ cm.

Step3: Calculate area

The area of a right - triangle $A=\frac{1}{2}\times base\times height$. Here, base $MN = 8$ cm and height $LM = 6$ cm. So $A=\frac{1}{2}\times6\times8 = 24$ $cm^{2}$.

Answer:

C. $24\ cm^{2}$

Question 21

Brief Explanations:

Statement P says all students offering Literature (L) also offer History (H), so the set of Literature students is a subset of the set of History students. Statement Q says students offering History (H) do not offer Geography (G), so the sets of History and Geography students are disjoint. Option C shows L as a subset of H and H and G as disjoint sets.