在\triangle{ABC} 中,内角A,B,C的对边分别为a,b,c,且2c-a=2bcosA,b=3.(I)求B的大小; (II)若a=\sqrt{3} ,求\tr
(1)由于在\triangle{ABC}中:b^2+c^2-a^2=bc,根据余弦定理,可得\cos A=b^2+c^2-a^2\over2bc,故可知,\cos A=1\over2。又因为A\in(0,\pi),所以A={\pi\over3}; (2)根据第一问可知,A={\pi\over3},故\sin A={{\sqrt3}\over2},b^2+c^2-7=bc,即b^2+c^2-bc=7\geqslant 2bc...
Letd(P,OA)≤min{d(P,AB),d(P,BC),d(P,OC)}where d denotes the distance from the point to the corresponding line and S be the region consisting of all those points P inside the rectangleOABCsuch thatO=(0,0),A=(3,0),B=(3,2)andC=(0,2),which satisfy the above relation, ...
Example 4 – Calculating the Length of the Hypotenuse of a Right-Angled Triangle To calculate the length of the hypotenuse, enter the following formula. =SQRT(C5^2+D5^2 ) PressEnter. Drag theFill Handleicon to fill the other cells with the formulas. Example 5 – Calculating Standard Deviati...
You would have to usesqrt()on the hypotenuse, c2, to have the length. Another way we could rewrite the pythagorean theorem is c= √a2+ b2. Let’s imagine we ran a circuit at our local park in the form of a triangle. We ran lengthwise and widthwise, then cut across back to our ...
在\triangle{ABC} 中,内角A, B,C的对边分别为a, b,c,已知a=\sqrt {3},b=\frac {2}{3},A=\frac {\pi }{3}.(1)求sinB的值;(2)求sin(\frac {\pi }{6}+B)的值. 相关知识点: 试题来源: 解析 (1)由正弦定理得:$$ \frac { \sin B } { b } = \frac { \sin A } { a ...
解:在\triangle ABC中,A为锐角,由余弦定理可得4=8+c^{2}-4 \sqrt {2}c×\cos A,即 c^{2}-4 \sqrt {2}c×\cos A+4=0 有解,∴判别式\triangle =32\cos ^{2}A-16\geqslant 0,∴\cos A\geqslant \dfrac { \sqrt {2}}{2},∴0 < A\leqslant 45^{\circ},故选:B.根据大边...
Step by step video solution for Let O(0,0),A(2,0),a n dB(1 1/(sqrt(3))) be the vertices of a triangle. Let R be the region consisting of all those points P inside O A B which satisfy d(P , O A)lt=min[d(p ,O B),d(P ,A B)] , where d denotes the distance fro...
Step by step video & image solution for Let O(0,0),A(2,0),a n dB(1 1/(sqrt(3))) be the vertices of a triangle. Let R be the region consisting of all those points P inside O A B which satisfy d(P , O A)lt=min[d(p ,O B),d(P ,A B)] , where d denotes the di...
Find the value of x as shown in the triangle below. x = (Simplify your answer. Type an exact answer, using radicals as needed. Rationalize all denominators.) Find the exact value of cos(\pi/4 - \pi/3) . (A) \sqrt 2 + \sqrt 6/2 ; (B) \sqrt 2 - \sqrt 6/4 : (C) \sq...